{"id":283,"date":"2021-07-14T15:59:06","date_gmt":"2021-07-14T15:59:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-6\/"},"modified":"2023-12-05T09:36:18","modified_gmt":"2023-12-05T09:36:18","slug":"section-exercises-6","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-6\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"

Null and Alternative Hypotheses - Practice<\/h2>\r\n
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1. You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. What is the random variable? Describe in words.<\/p>\r\n2. You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.<\/span>\r\n\r\n3 . The American family has an average of two children. What is the random variable? Describe in words.<\/span>\r\n\r\n4.\u00a0The mean entry-level salary of an employee at a company is $58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses.<\/span>\r\n\r\n5. A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually less. What is the random variable? Describe in words.<\/span>\r\n\r\n6. A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.<\/span>\r\n\r\n7. In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.<\/span>\r\n\r\n8. Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.<\/span>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>

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  1. H0<\/sub><\/em>: ________<\/li>\r\n \t
  2. Ha<\/sub><\/em>: ________<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
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    9. A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be?<\/p>\r\n\r\n

      \r\n \t
    1. H0<\/sub><\/em>: __________<\/li>\r\n \t
    2. Ha<\/sub><\/em>: __________<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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      \r\n\r\n10. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?\r\n
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      1. H0<\/sub><\/em>: ________<\/li>\r\n \t
      2. Ha<\/sub><\/em>: ________<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n

        Outcomes and the Type I and Type II Errors - Practice<\/h2>\r\n11.\u00a0The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.\r\n\r\n
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        12. A sleeping bag is tested to withstand temperatures of \u201315 \u00b0F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.<\/p>\r\n13. For Exercise 12,\u00a0what are \u03b1 and \u03b2 in words?\r\n\r\n14. In words, describe 1 \u2013 \u03b2 for Exercise 12.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        15. A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H0<\/sub><\/em>, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        16. A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H0<\/sub><\/em>, is: the surgical procedure will go well. Which is the error with the greater consequence?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        \r\n\r\n17. The power of a test is 0.981. What is the probability of a Type II error?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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        18. A group of divers is exploring an old sunken ship. Suppose the null hypothesis, H0<\/sub><\/em>, is: the sunken ship does not contain buried treasure. State the Type I and Type II errors in complete sentences.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        19. A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H0<\/sub><\/em>, is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        \r\n\r\n20. A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H0<\/sub><\/em>, is: the sample contains E-coli. Which is the error with the greater consequence?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n

        Distribution Needed for Hypothesis Testing - Practice<\/h2>\r\n
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        \r\n\r\n21. Which two distributions can you use for hypothesis testing for this chapter?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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        22. Which distribution do you use when you are testing a population mean and the standard deviation is known? Assume the sample size is large.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        \r\n\r\n23. Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume the sample size is large.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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        \r\n\r\n24. A population mean is 13. The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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        25. A population has a mean is 25 and a standard deviation of five. The sample mean is 24, and the sample size is 108. What distribution should you use to perform a hypothesis test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        26. It is thought that 42% of respondents in a taste test would prefer Brand A<\/em>. In a particular test of 100 people, 39% preferred Brand A<\/em>. What distribution should you use to perform a hypothesis test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        27. You are performing a hypothesis test of a single population mean using a Student\u2019s t<\/em>-distribution. What must you assume about the distribution of the data?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        28. You are performing a hypothesis test of a single population mean using a Student\u2019s t<\/em>-distribution. The data are not from a simple random sample. Can you accurately perform the hypothesis test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        29. You are performing a hypothesis test of a single population proportion. What must be true about the quantities of np<\/em> and nq<\/em>?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        \r\n\r\n30. You are performing a hypothesis test of a single population proportion. You find out that np<\/em> is less than five. What must you do to be able to perform a valid hypothesis test?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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        31. You are performing a hypothesis test of a single population proportion. The data come from which distribution?<\/p>\r\n\r\n<\/div>\r\n

        Rare Events, the Sample, Decision and Conclusion - Practice<\/h2>\r\n<\/section><\/div>\r\n
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        32. When do you reject the null hypothesis?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        33. The probability of winning the grand prize at a particular carnival game is 0.005. Is the outcome of winning very likely or very unlikely?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        34. The probability of winning the grand prize at a particular carnival game is 0.005. Michele wins the grand prize. Is this considered a rare or common event? Why?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        35. It is believed that the mean height of high school students who play basketball on the school team is 73 inches with a standard deviation of 1.8 inches. A random sample of 40 players is chosen. The sample mean was 71 inches, and the sample standard deviation was 1.5 years. Do the data support the claim that the mean height is less than 73 inches? The p<\/em>-value is almost zero. State the null and alternative hypotheses and interpret the p<\/em>-value.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        36. The mean age of graduate students at a University is at most 31 years with a standard deviation of two years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1% level? The p<\/em>-value is 0.0264. State the null and alternative hypotheses and interpret the p<\/em>-value.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        37. Does the shaded region represent a low or a high p<\/em>-value compared to a level of significance of 1%?<\/p>\r\n\r\n

        \"A<\/span><\/figure>\r\n<\/div>\r\n
        <\/div>\r\n<\/section><\/div>\r\n
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        38. What should you do when \u03b1<\/em> > p<\/em>-value?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        39. What should you do if \u03b1<\/em> = p<\/em>-value?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        40. If you do not reject the null hypothesis, then it must be true. Is this statement correct? State why or why not in complete sentences.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the following information to answer the next seven exercises:<\/em> Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was three years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal.\r\n

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        41. Is this a test of means or proportions?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        42. What symbol represents the random variable for this test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        43. In words, define the random variable for this test.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        44. Is the population standard deviation known and, if so, what is it?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        45. Calculate the following:<\/p>\r\n\r\n

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        1. [latex]\\overline{x}[\/latex]_______<\/li>\r\n \t
        2. \u03c3<\/em> _______<\/li>\r\n \t
        3. sx<\/sub><\/em> _______<\/li>\r\n \t
        4. n<\/em> _______<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
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          \r\n\r\n46. Since both \u03c3 and\u00a0sx\u00a0<\/sub><\/em>are given, which should be used? In one to two complete sentences, explain why.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
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          47. State the distribution to use for the hypothesis test.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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          48. A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.<\/p>\r\n\r\n

            \r\n \t
          1. Is this a test of one mean or proportion?<\/li>\r\n \t
          2. State the null and alternative hypotheses.\r\nH0<\/sub><\/em>: ____________________ Ha<\/sub><\/em> : ____________________<\/li>\r\n \t
          3. Is this a right-tailed, left-tailed, or two-tailed test?<\/li>\r\n \t
          4. What symbol represents the random variable for this test?<\/li>\r\n \t
          5. In words, define the random variable for this test.<\/li>\r\n \t
          6. Is the population standard deviation known and, if so, what is it?<\/li>\r\n \t
          7. Calculate the following:\r\n
              \r\n \t
            1. [latex]\\overline{x}[\/latex]= _____________<\/li>\r\n \t
            2. s<\/em> = ____________<\/li>\r\n \t
            3. n<\/em> = ____________<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            4. Which test should be used?<\/li>\r\n \t
            5. State the distribution to use for the hypothesis test.<\/li>\r\n \t
            6. Find the p<\/em>-value.<\/li>\r\n \t
            7. At a pre-conceived \u03b1<\/em> = 0.05, what is your:\r\n
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              1. Decision:<\/li>\r\n \t
              2. Reason for the decision:<\/li>\r\n \t
              3. Conclusion (write out in a complete sentence):<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n

                Additional Information and Full Hypothesis Test Examples - Practice<\/h2>\r\n49.\u00a0Assume H0<\/sub><\/em>: \u03bc<\/em> = 9 and Ha<\/sub><\/em>: \u03bc<\/em> < 9. Is this a left-tailed, right-tailed, or two-tailed test?\r\n\r\n50. Assume <\/span>H0<\/sub><\/em>: <\/span>\u03bc<\/em> \u2264 6 and <\/span>Ha<\/sub><\/em>: <\/span>\u03bc<\/em> > 6. Is this a left-tailed, right-tailed, or two-tailed test<\/span>\r\n\r\n51. Assume <\/span>H0<\/sub><\/em>: <\/span>p<\/em> = 0.25 and <\/span>Ha<\/sub><\/em>: <\/span>p<\/em> \u2260 0.25. Is this a left-tailed, right-tailed, or two-tailed test?<\/span>\r\n\r\n52. Draw the general graph of a left-tailed test.<\/span>\r\n\r\n53. Draw the graph of a two-tailed test.<\/span>\r\n\r\n54. A bottle of water is labeled as containing 16 fluid ounces of water. You believe it is less than that. What type of test would you use?<\/span>\r\n\r\n55. Your friend claims that his mean golf score is 63. You want to show that it is higher than that. What type of test would you use?<\/span>\r\n\r\n56. A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that accurate. What type of test would you use?<\/span>\r\n\r\n57. You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you think it is less for this particular coin. What type of test would you use?<\/span>\r\n\r\n58. If the alternative hypothesis has a not equals ( \u2260 ) symbol, which type of test would you use?<\/span>\r\n\r\n59. Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?<\/span>\r\n\r\n60. Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?<\/span>\r\n\r\n61. Assume the null hypothesis states that the mean is equal to 88. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test?<\/span>\r\n

                Null and Alternative Hypotheses - Homework<\/h2>\r\n
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                62. Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.\u00a0State the null hypothesis, H0<\/sub><\/em>, and the alternative hypothesis. Ha<\/sub><\/em>, in terms of the appropriate parameter (\u03bc<\/em> or p<\/em>).<\/p>\r\n\r\n

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                1. The mean number of years Americans work before retiring is 34.<\/li>\r\n \t
                2. At most, 60% of Americans vote in presidential elections.<\/li>\r\n \t
                3. The mean starting salary for San Jose State University graduates is at least $100,000 per year.<\/li>\r\n \t
                4. Twenty-nine percent of high school seniors get drunk each month.<\/li>\r\n \t
                5. Fewer than 5% of adults ride the bus to work in Los Angeles.<\/li>\r\n \t
                6. The mean number of cars a person owns in her lifetime is not more than ten.<\/li>\r\n \t
                7. About half of Americans prefer to live away from cities, given the choice.<\/li>\r\n \t
                8. Europeans have a mean paid vacation each year of six weeks.<\/li>\r\n \t
                9. The chance of developing breast cancer is under 11% for women.<\/li>\r\n \t
                10. Private universities' mean tuition cost is more than $20,000 per year.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                  63. Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of teen girls smoke to stay thin? The alternative hypothesis is:<\/p>\r\n\r\n

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                  1. p<\/em> < 0.30<\/li>\r\n \t
                  2. p<\/em> \u2264 0.30<\/li>\r\n \t
                  3. p<\/em> \u2265 0.30<\/li>\r\n \t
                  4. p<\/em> > 0.30<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                    64. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:<\/p>\r\n\r\n

                      \r\n \t
                    1. p<\/em> = 0.20<\/li>\r\n \t
                    2. p<\/em> > 0.20<\/li>\r\n \t
                    3. p<\/em> < 0.20<\/li>\r\n \t
                    4. p<\/em> \u2264 0.20<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                      65. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:<\/p>\r\n\r\n

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                      1. Ho<\/sub><\/em>:[latex]\\overline{x}[\/latex]\u00a0= 4.5, Ha<\/sub><\/em> :[latex]\\overline{x}[\/latex]\u00a0> 4.5<\/li>\r\n \t
                      2. Ho<\/sub><\/em>: \u03bc<\/em> \u2265 4.5, Ha<\/sub><\/em>: \u03bc<\/em> < 4.5<\/li>\r\n \t
                      3. Ho<\/sub><\/em>: \u03bc<\/em> = 4.75, Ha<\/sub><\/em>: \u03bc<\/em> > 4.75<\/li>\r\n \t
                      4. Ho<\/sub><\/em>: \u03bc<\/em> = 4.5, Ha<\/sub><\/em>: \u03bc<\/em> > 4.5<\/li>\r\n<\/ol>\r\n

                        Outcomes and the Type I and Type II Errors - Homework<\/h2>\r\n
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                        \r\n\r\n66. State the Type I and Type II errors in complete sentences given the following statements.\r\n
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                        1. The mean number of years Americans work before retiring is 34.<\/li>\r\n \t
                        2. At most 60% of Americans vote in presidential elections.<\/li>\r\n \t
                        3. The mean starting salary for San Jose State University graduates is at least $100,000 per year.<\/li>\r\n \t
                        4. Twenty-nine percent of high school seniors get drunk each month.<\/li>\r\n \t
                        5. Fewer than 5% of adults ride the bus to work in Los Angeles.<\/li>\r\n \t
                        6. The mean number of cars a person owns in his or her lifetime is not more than ten.<\/li>\r\n \t
                        7. About half of Americans prefer to live away from cities, given the choice.<\/li>\r\n \t
                        8. Europeans have a mean paid vacation each year of six weeks.<\/li>\r\n \t
                        9. The chance of developing breast cancer is under 11% for women.<\/li>\r\n \t
                        10. Private universities mean tuition cost is more than $20,000 per year.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                          \r\n\r\n67. For statements 1-10 in 66, answer the following in complete sentences.\r\n
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                          1. State a consequence of committing a Type I error.<\/li>\r\n \t
                          2. State a consequence of committing a Type II error.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                            68. When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is \u201cthe drug is unsafe.\u201d What is the Type II Error?<\/p>\r\n\r\n

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                            1. To conclude the drug is safe when in, fact, it is unsafe.<\/li>\r\n \t
                            2. Not to conclude the drug is safe when, in fact, it is safe.<\/li>\r\n \t
                            3. To conclude the drug is safe when, in fact, it is safe.<\/li>\r\n \t
                            4. Not to conclude the drug is unsafe when, in fact, it is unsafe.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                              69. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.<\/p>\r\n\r\n

                                \r\n \t
                              1. at least 20%, when in fact, it is less than 20%.<\/li>\r\n \t
                              2. 20%, when in fact, it is 20%.<\/li>\r\n \t
                              3. less than 20%, when in fact, it is at least 20%.<\/li>\r\n \t
                              4. less than 20%, when in fact, it is less than 20%.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
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                                70. It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?<\/p>\r\nThe Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours\r\n

                                  \r\n \t
                                1. is more than seven hours.<\/li>\r\n \t
                                2. is at most seven hours.<\/li>\r\n \t
                                3. is at least seven hours.<\/li>\r\n \t
                                4. is less than seven hours.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
                                  \r\n
                                  \r\n

                                  71. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:<\/p>\r\n\r\n

                                    \r\n \t
                                  1. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher<\/li>\r\n \t
                                  2. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same<\/li>\r\n \t
                                  3. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher<\/li>\r\n \t
                                  4. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher<\/li>\r\n<\/ol>\r\n

                                    Distribution Needed for Hypothesis Testing - Homework<\/h2>\r\n
                                    \r\n
                                    \r\n
                                    \r\n

                                    72. It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is[latex]\\overline{X}[\/latex] ~ ________________<\/p>\r\n\r\n

                                      \r\n \t
                                    1. N[latex]\\left(7.24,\\frac{{1.93}}{{\\sqrt{22}}}\\right)[\/latex]<\/li>\r\n \t
                                    2. N(7.24,1.93)<\/li>\r\n \t
                                    3. t<\/em>22<\/sub><\/li>\r\n \t
                                    4. t<\/em>21<\/sub><\/li>\r\n<\/ol>\r\n<\/div>\r\n
                                      \r\n
                                      \r\n
                                      \r\n

                                      Rare Events, the Sample, Decision and Conclusion - Homework<\/h2>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>
                                      \r\n

                                      73. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.<\/p>\r\n\r\n

                                      \r\n
                                      \r\n
                                        \r\n \t
                                      1. Is this a test of one mean or proportion?<\/li>\r\n \t
                                      2. State the null and alternative hypotheses.\r\nH0<\/sub><\/em>: ____________________ Ha<\/sub><\/em>: ____________________<\/li>\r\n \t
                                      3. Is this a right-tailed, left-tailed, or two-tailed test?<\/li>\r\n \t
                                      4. What symbol represents the random variable for this test?<\/li>\r\n \t
                                      5. In words, define the random variable for this test.<\/li>\r\n \t
                                      6. Calculate the following:\r\n
                                          \r\n \t
                                        1. x<\/em> = ________________<\/li>\r\n \t
                                        2. n<\/em> = ________________<\/li>\r\n \t
                                        3. p<\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span> = _____________<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
                                        4. Calculate \u03c3x<\/sub><\/em> = __________. Show the formula set-up.<\/li>\r\n \t
                                        5. State the distribution to use for the hypothesis test.<\/li>\r\n \t
                                        6. Find the p<\/em>-value.<\/li>\r\n \t
                                        7. At a pre-conceived \u03b1<\/em> = 0.05, what is your:\r\n
                                            \r\n \t
                                          1. Decision:<\/li>\r\n \t
                                          2. Reason for the decision:<\/li>\r\n \t
                                          3. Conclusion (write out in a complete sentence):<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                                            Additional Information and Full Hypothesis Test Examples - Homework<\/h2>\r\n<\/div>\r\n<\/section>
                                            \r\n

                                            For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in [link]<\/a>. Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.<\/em><\/p>\r\n\r\n

                                            \r\n
                                            NOTE<\/div>\r\n<\/header>
                                            \r\n

                                            If you are using a Student's-t<\/em> distribution for one of the following homework problems, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, however.)<\/p>\r\n\r\n<\/section><\/div>\r\n

                                            \r\n
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                                            74. A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n\r\n75. From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
                                            \r\n
                                            \r\n

                                            76. The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of 20\u00a2. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95\u00a2 with a standard deviation of 18\u00a2. Do the data support the claim at the 1% level?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n

                                            77. An article in the San Jose Mercury News<\/em> stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n\r\n78. The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let x<\/em> = the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
                                            \r\n
                                            \r\n

                                            79. In 1955, Life Magazine<\/em> reported that the 25-year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n

                                            80. Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n\r\n81. A Nissan Motor Corporation advertisement read, \u201cThe average man\u2019s I.Q. is 107. The average brown trout\u2019s I.Q. is 4. So why can\u2019t man catch brown trout?\u201d Suppose you believe that the brown trout\u2019s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief.\r\n\r\n82. Refer to Exercise 81.\u00a0Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout\u2019s mean I.Q. is not four.\r\n\r\n83. According to an article in <\/span>Newsweek<\/em>, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don\u2019t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percentage of girls born in China is 46.7?<\/span>\r\n\r\n84. A poll done for <\/span>Newsweek<\/em> found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percentage is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent\u2019s survey, would you agree with the <\/span>Newsweek<\/em> poll? In complete sentences, also give three reasons why the two polls might give different results.<\/span>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
                                            \r\n
                                            \r\n

                                            85. The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it\u2019s shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours?<\/p>\r\n

                                            Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            \r\n
                                            \r\n\r\n86. Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percentage at her school is less than 40%.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n
                                            \r\n
                                            \r\n

                                            87. Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if 68% also represents California\u2019s percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in California, was randomly selected for comparison. In the same year, 34 of the 44 online courses LBCC offered were taught by full-time faculty. Conduct a hypothesis test to determine if 68% represents California. NOTE: For more accurate results, use more California community colleges and this past year's data.<\/p>\r\n88\u00a0<\/span>.\u00a0<\/span>Use the \u201cLap time\u201d data for Lap 4 (see\u00a0<\/span>[link]<\/a>) to test the claim that Terri finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given.<\/span>\r\n\r\n89<\/span>\u00a0<\/span>.\u00a0<\/span>Use the \u201cInitial Public Offering\u201d data (see\u00a0<\/span>[link]<\/a>) to test the claim that the mean offer price was $18 per share. Do not use all the data. Use your random number generator to randomly survey 15 prices.<\/span>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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                                            90. \"Asian Family Reunion,\" by Chau Nguyen<\/p>\r\n

                                            Every two years it comes around.\r\nWe all get together from different towns.\r\nIn my honest opinion,\r\nIt's not a typical family reunion.\r\nNot forty, or fifty, or sixty,\r\nBut how about seventy companions!\r\nThe kids would play, scream, and shout\r\nOne minute they're happy, another they'll pout.\r\nThe teenagers would look, stare, and compare\r\nFrom how they look to what they wear.\r\nThe men would chat about their business\r\nThat they make more, but never less.\r\nMoney is always their subject\r\nAnd there's always talk of more new projects.\r\nThe women get tired from all of the chats\r\nThey head to the kitchen to set out the mats.\r\nSome would sit and some would stand\r\nEating and talking with plates in their hands.\r\nThen come the games and the songs\r\nAnd suddenly, everyone gets along!\r\nWith all that laughter, it's sad to say\r\nThat it always ends in the same old way.\r\nThey hug and kiss and say \"good-bye\"\r\nAnd then they all begin to cry!\r\nI say that 60 percent shed their tears\r\nBut my mom counted 35 people this year.\r\nShe said that boys and men will always have their pride,\r\nSo we won't ever see them cry.\r\nI myself don't think she's correct,\r\nSo could you please try this problem to see if you object?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            <\/header>
                                            \r\n
                                            \r\n\r\n91<\/span>.\u00a0<\/span>\"The Problem with Angels,\" by Cyndy Dowling<\/span>\r\n
                                            \r\n

                                            Although this problem is wholly mine,\r\nThe catalyst came from the magazine, Time.\r\nOn the magazine cover I did find\r\nThe realm of angels tickling my mind.\r\nInside, 69% I found to be\r\nIn angels, Americans do believe.\r\nThen, it was time to rise to the task,\r\nNinety-five high school and college students I did ask.\r\nViewing all as one group,\r\nRandom sampling to get the scoop.\r\nSo, I asked each to be true,\r\n\"Do you believe in angels?\" Tell me, do!\r\nHypothesizing at the start,\r\nTotally believing in my heart\r\nThat the proportion who said yes\r\nWould be equal on this test.\r\nLo and behold, seventy-three did arrive,\r\nOut of the sample of ninety-five.\r\nNow your job has just begun,\r\nSolve this problem and have some fun.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            <\/header>
                                            \r\n
                                            \r\n\r\n92.\u00a0<\/span>\"Blowing Bubbles,\" by Sondra Prull<\/span>\r\n
                                            \r\n

                                            Studying stats just made me tense,\r\nI had to find some sane defense.\r\nSome light and lifting simple play\r\nTo float my math anxiety away.\r\nBlowing bubbles lifts me high\r\nTakes my troubles to the sky.\r\nPOIK! They're gone, with all my stress\r\nBubble therapy is the best.\r\nThe label said each time I blew\r\nThe average number of bubbles would be at least 22.\r\nI blew and blew and this I found\r\nFrom 64 blows, they all are round!\r\nBut the number of bubbles in 64 blows\r\nVaried widely, this I know.\r\n20 per blow became the mean\r\nThey deviated by 6, and not 16.\r\nFrom counting bubbles, I sure did relax\r\nBut now I give to you your task.\r\nWas 22 a reasonable guess?\r\nFind the answer and pass this test!<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            <\/header>
                                            \r\n
                                            \r\n\r\n93.\u00a0<\/span>\"Dalmatian Darnation,\" by Kathy Sparling<\/span>\r\n
                                            \r\n

                                            A greedy dog breeder named Spreckles\r\nBred puppies with numerous freckles\r\nThe Dalmatians he sought\r\nPossessed spot upon spot\r\nThe more spots, he thought, the more shekels.\r\nHis competitors did not agree\r\nThat freckles would increase the fee.\r\nThey said, \u201cSpots are quite nice\r\nBut they don't affect price;\r\nOne should breed for improved pedigree.\u201d\r\nThe breeders decided to prove\r\nThis strategy was a wrong move.\r\nBreeding only for spots\r\nWould wreak havoc, they thought.\r\nHis theory they want to disprove.\r\nThey proposed a contest to Spreckles\r\nComparing dog prices to freckles.\r\nIn records they looked up\r\nOne hundred one pups:\r\nDalmatians that fetched the most shekels.\r\nThey asked Mr. Spreckles to name\r\nAn average spot count he'd claim\r\nTo bring in big bucks.\r\nSaid Spreckles, \u201cWell, shucks,\r\nIt's for one hundred one that I aim.\u201d\r\nSaid an amateur statistician\r\nWho wanted to help with this mission.\r\n\u201cTwenty-one for the sample\r\nStandard deviation's ample:\r\nThey examined one hundred and one\r\nDalmatians that fetched a good sum.\r\nThey counted each spot,\r\nMark, freckle and dot\r\nAnd tallied up every one.\r\nInstead of one hundred one spots\r\nThey averaged ninety six dots\r\nCan they muzzle Spreckles\u2019\r\nObsession with freckles\r\nBased on all the dog data they've got?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n

                                            <\/header>
                                            \r\n
                                            \r\n\r\n94.\u00a0<\/span>\"Macaroni and Cheese, please!!\" by Nedda Misherghi and Rachelle Hall<\/span>\r\n
                                            \r\n

                                            As a poor starving student I don't have much money to spend for even the bare necessities. So my favorite and main staple food is macaroni and cheese. It's high in taste and low in cost and nutritional value.<\/p>\r\n

                                            One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! $2.02 !!! Can you believe it? It made me stop and think. The world is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantic-family-value-pack) was at most $1, but now I wasn't so sure. However, I was determined to find out. I went to 53 of the closest grocery stores and surveyed the prices of macaroni and cheese. Here are the data I wrote in my notebook:<\/p>\r\n\r\n

                                            \r\n
                                            Price per box of Mac and Cheese:<\/strong><\/div>\r\n