{"id":291,"date":"2021-07-14T15:59:08","date_gmt":"2021-07-14T15:59:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-5\/"},"modified":"2023-12-05T09:41:14","modified_gmt":"2023-12-05T09:41:14","slug":"section-exercises-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/section-exercises-5\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"
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Two Population Means with Unknown Standard Deviations - Practice<\/h2>\r\n

Use the following information to answer the next 15 exercises:<\/em> Indicate if the hypothesis test is for<\/p>\r\n\r\n

    \r\n \t
  1. independent group means, population standard deviations, and\/or variances known<\/li>\r\n \t
  2. independent group means, population standard deviations, and\/or variances unknown<\/li>\r\n \t
  3. matched or paired samples<\/li>\r\n \t
  4. single mean<\/li>\r\n \t
  5. two proportions<\/li>\r\n \t
  6. single proportion<\/li>\r\n<\/ol>\r\n

    1. It is believed that 70% of males pass their driver's test in the first attempt, while 65% of females pass the test in the first attempt. Of interest is whether the proportions are in fact equal.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    2. A new laundry detergent is tested on consumers. Of interest is the proportion of consumers who prefer the new brand over the leading competitor. A study is done to test this.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    3. A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    4. The known standard deviation in salary for all mid-level professionals in the financial industry is $11,000. Company A and Company B are in the financial industry. Suppose samples are taken of mid-level professionals from Company A and from Company B. The sample mean salary for mid-level professionals in Company A is $80,000. The sample mean salary for mid-level professionals in Company B is $96,000. Company A and Company B management want to know if their mid-level professionals are paid differently, on average.<\/p>\r\n5.\u00a0The average worker in Germany gets eight weeks of paid vacation.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    6. According to a television commercial, 80% of dentists agree that Ultrafresh toothpaste is the best on the market.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    7. It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of 31 females had a mean score of 82 with a standard deviation of three, and a random sample of 25 males had a mean score of 76 with a standard deviation of four.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    8. The league mean batting average is 0.280 with a known standard deviation of 0.06. The Rattlers and the Vikings belong to the league. The mean batting average for a sample of eight Rattlers is 0.210, and the mean batting average for a sample of eight Vikings is 0.260. There are 24 players on the Rattlers and 19 players on the Vikings. Are the batting averages of the Rattlers and Vikings statistically different?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    9. In a random sample of 100 forests in the United States, 56 were coniferous or contained conifers. In a random sample of 80 forests in Mexico, 40 were coniferous or contained conifers. Is the proportion of conifers in the United States statistically more than the proportion of conifers in Mexico?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    10. A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means hours slept for each person were recorded before starting the medication and after.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    11. It is thought that teenagers sleep more than adults on average. A study is done to verify this. A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.<\/p>\r\n12.\u00a0Varsity athletes practice five times a week, on average.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    13. A sample of 12 in-state graduate school programs at school A has a mean tuition of $64,000 with a standard deviation of $8,000. At school B, a sample of 16 in-state graduate programs has a mean of $80,000 with a standard deviation of $6,000. On average, are the mean tuitions different?<\/p>\r\n\r\n<\/div>\r\n

    14. A new WiFi range booster is being offered to consumers. A researcher tests the native range of 12 different routers under the same conditions. The ranges are recorded. Then the researcher uses the new WiFi range booster and records the new ranges. Does the new WiFi range booster do a better job?<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n
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    <\/div>\r\n
    15. A high school principal claims that 30% of student-athletes drive themselves to school, while 4% of non-athletes drive themselves to school. In a sample of 20 student-athletes, 45% drive themselves to school. In a sample of 35 non-athlete students, 6% drive themselves to school. Is the percent of student-athletes who drive themselves to school more than the percent of non-athletes?<\/span><\/div>\r\n<\/section><\/div>\r\n
    <\/div>\r\nUse the following information to answer the next three exercises:<\/em> A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions.\r\n
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    16. Are standard deviations known or unknown?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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    17. What is the random variable?<\/p>\r\n\r\n<\/div>\r\n

    18. Is this a one-tailed or two-tailed test?<\/div>\r\n
    <\/div>\r\n
    Use the following information to answer the next 12 exercises:<\/em> The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for Whites born in 1900 and 33.0 years for non-Whites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 Whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 non-Whites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for Whites and non-Whites.<\/span><\/div>\r\n<\/section><\/div>\r\n
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    19. Is this a test of means or proportions?<\/p>\r\n\r\n<\/div>\r\n

    20. State the null and alternative hypotheses.<\/div>\r\n<\/section><\/div>\r\n
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      \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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      21. Is this a right-tailed, left-tailed, or two-tailed test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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      22. In symbols, what is the random variable of interest for this test?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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      23. In words, define the random variable of interest for this test.<\/p>\r\n\r\n<\/div>\r\n

      24. Which distribution (normal or Student's t<\/em>) would you use for this hypothesis test?<\/div>\r\n<\/section>\r\n
      <\/div>\r\n
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      25. Explain why you chose the distribution you did for Exercise 24.<\/div>\r\n<\/section>\r\n
      <\/div>\r\n
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      26. Calculate the test statistic and p<\/em>-value.<\/div>\r\n<\/section>\r\n
      <\/div>\r\n
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      27. Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p<\/em>-value.<\/div>\r\n<\/section>\r\n
      <\/div>\r\n
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      28. Find the p<\/em>-value.<\/div>\r\n<\/section>\r\n
      <\/div>\r\n
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      29. At a pre-conceived <\/span>\u03b1<\/em> = 0.05, what is your:<\/span><\/div>\r\n<\/section><\/div>\r\n
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        \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<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
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        30. Does it appear that the means are the same? Why or why not?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n

        Two Population Means with Known Standard Deviations - Practice<\/h2>\r\n
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        Use the following information to answer the next five exercises.<\/em> The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. The table\u00a0shows the result. Scouters believe that Rodriguez pitches a speedier fastball.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        Pitcher<\/th>\r\nSample Mean Speed of Pitches (mph)<\/th>\r\nPopulation Standard Deviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
        Wesley<\/td>\r\n86<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
        Rodriguez<\/td>\r\n91<\/td>\r\n7<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

        31. What is the random variable?<\/p>\r\n\r\n<\/div>\r\n

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        32. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        33. What is the test statistic?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

        34. What is the p<\/em>-value?<\/div>\r\n
        <\/div>\r\n
        35. At the 1% significance level, what is your conclusion?<\/span><\/div>\r\n
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        <\/div>\r\n
        Use the following information to answer the next five exercises.<\/em> A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        Plant Group<\/th>\r\nSample Mean Height of Plants (inches)<\/th>\r\nPopulation Standard Deviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
        Food<\/td>\r\n16<\/td>\r\n2.5<\/td>\r\n<\/tr>\r\n
        No food<\/td>\r\n14<\/td>\r\n1.5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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        36. Is the population standard deviation known or unknown?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        37. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

        38. What is the p<\/em>-value?<\/div>\r\n
        <\/div>\r\n
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        39. Draw the graph of the p<\/em>-value.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        40. At the 1% significance level, what is your conclusion<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the following information to answer the next five exercises.<\/em> Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        <\/th>\r\nSample Mean Melting Temperatures (\u00b0F)<\/th>\r\nPopulation Standard Deviation<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
        Alloy Gamma<\/td>\r\n800<\/td>\r\n95<\/td>\r\n<\/tr>\r\n
        Alloy Zeta<\/td>\r\n900<\/td>\r\n105<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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        41. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n

        42. Is this a right-, left-, or two-tailed test?<\/div>\r\n
        <\/div>\r\n
        43. What is the <\/span>p<\/em>-value?<\/span><\/div>\r\n<\/section><\/div>\r\n
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        <\/div>\r\n
        44. Draw the graph of the p<\/em>-value.<\/div>\r\n<\/section><\/div>\r\n
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        45. At the 1% significance level, what is your conclusion?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

        Comparing Two Independent Population Proportions - Practice<\/h2>\r\n
        Use the following information for the next five exercises.<\/em> Two types of phone operating systems are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1<\/sub> had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2<\/sub> had system failures within the first eight hours of operation. OS2<\/sub> is believed to be more stable (have fewer crashes) than OS1<\/sub>.\r\n
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        46. Is this a test of means or proportions?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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        47. What is the random variable?<\/p>\r\n\r\n<\/div>\r\n

        48. State the null and alternative hypotheses.<\/div>\r\n<\/section>\r\n
        <\/div>\r\n
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        49. What is the <\/span>p<\/em>-value?<\/span><\/div>\r\n<\/section><\/div>\r\n
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        <\/div>\r\n
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        50. What can you conclude about the two operating systems?<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n
        <\/div>\r\n
        Use the following information to answer the next twelve exercises.<\/em> In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.\r\n
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        51. Is this a test of means or proportions?<\/p>\r\n\r\n<\/div>\r\n

        52. State the null and alternative hypotheses.<\/div>\r\n<\/section><\/div>\r\n
        \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
          \r\n
          \r\n\r\n53. Is this a right-tailed, left-tailed, or two-tailed test? How do you know?\r\n\r\n<\/div>\r\n
          54. What is the random variable of interest for this test?<\/div>\r\n<\/section>\r\n
          <\/div>\r\n
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          55. In words, define the random variable for this test.<\/span><\/div>\r\n<\/section>\r\n
          <\/div>\r\n
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          56. Which distribution (normal or Student's <\/span>t<\/em>) would you use for this hypothesis test?<\/span><\/div>\r\n<\/section>\r\n
          <\/div>\r\n
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          57. Explain why you chose the distribution you did.<\/span><\/div>\r\n<\/section><\/div>\r\n
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          <\/div>\r\n
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          58. Calculate the test statistic.<\/div>\r\n<\/section>\r\n
          <\/div>\r\n
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          59. Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the <\/span>p<\/em>-value.<\/span><\/div>\r\n<\/section><\/div>\r\n
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          \"This<\/span><\/figure>\r\n<\/div>\r\n
          <\/div>\r\n<\/section><\/div>\r\n
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          60. Find the p<\/em>-value.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

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          61. At a pre-conceived \u03b1<\/em> = 0.05, what is your:<\/p>\r\n\r\n

          \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<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n
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            \r\n\r\n62. Does it appear that the proportion of Nevadans who are two or more races is higher than the proportion of North Dakotans? Why or why not?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>
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            Matched or Paired Samples - Practice<\/h2>\r\n<\/section>\r\n

            Use the following information to answer the next five exercises.<\/em> A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in the table below. The \u201cbefore\u201d value is matched to an \u201cafter\u201d value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Installation<\/th>\r\nA<\/th>\r\nB<\/th>\r\nC<\/th>\r\nD<\/th>\r\nE<\/th>\r\nF<\/th>\r\nG<\/th>\r\nH<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            Before<\/td>\r\n3<\/td>\r\n6<\/td>\r\n4<\/td>\r\n2<\/td>\r\n5<\/td>\r\n8<\/td>\r\n2<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
            After<\/td>\r\n1<\/td>\r\n5<\/td>\r\n2<\/td>\r\n0<\/td>\r\n1<\/td>\r\n0<\/td>\r\n2<\/td>\r\n2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
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            63. What is the random variable?<\/p>\r\n\r\n<\/div>\r\n

            64. State the null and alternative hypotheses.<\/div>\r\n<\/section>\r\n
            <\/div>\r\n
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            65. What is the <\/span>p<\/em>-value?<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
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            66. Draw the graph of the <\/span>p<\/em>-value.<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
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            67. What conclusion can you draw about the software patch?<\/span><\/div>\r\n<\/section><\/div>\r\n
            \r\n
            <\/div>\r\n
            \r\n
            Use the following information to answer the next five exercises.<\/em> A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level.<\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Subject<\/th>\r\nA<\/th>\r\nB<\/th>\r\nC<\/th>\r\nD<\/th>\r\nE<\/th>\r\nF<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            Before<\/td>\r\n3<\/td>\r\n4<\/td>\r\n3<\/td>\r\n2<\/td>\r\n4<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
            After<\/td>\r\n4<\/td>\r\n5<\/td>\r\n6<\/td>\r\n4<\/td>\r\n5<\/td>\r\n7<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
            \r\n
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            68. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

            \r\n
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            69. What is the p<\/em>-value?<\/p>\r\n\r\n<\/div>\r\n

            70. What is the sample mean difference?<\/div>\r\n<\/section>\r\n
            <\/div>\r\n
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            71. Draw the graph of the <\/span>p<\/em>-value.<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            72. What conclusion can you draw about the juggling class?<\/span><\/div>\r\n<\/section><\/div>\r\n
            <\/div>\r\n
            <\/div>\r\nUse the following information to answer the next five exercises.<\/em> A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Patient<\/th>\r\nA<\/th>\r\nB<\/th>\r\nC<\/th>\r\nD<\/th>\r\nE<\/th>\r\nF<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            Before<\/td>\r\n161<\/td>\r\n162<\/td>\r\n165<\/td>\r\n162<\/td>\r\n166<\/td>\r\n171<\/td>\r\n<\/tr>\r\n
            After<\/td>\r\n158<\/td>\r\n159<\/td>\r\n166<\/td>\r\n160<\/td>\r\n167<\/td>\r\n169<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
            \r\n
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            73. State the null and alternative hypotheses.<\/p>\r\n\r\n<\/div>\r\n

            74. What is the test statistic?<\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            75. What is the <\/span>p<\/em>-value?<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            76. What is the sample mean difference?<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            77. What is the conclusion?<\/span><\/div>\r\n<\/section><\/div>\r\n
            \r\n

            Two Population Means with Unknown Standard Deviations - Homework<\/h2>\r\n<\/section><\/div>\r\n
            DIRECTIONS: For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in Appendix E<\/a>.\u00a0<\/em>\r\n
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            NOTE<\/h3>\r\n<\/header>
            \r\n

            If you are using a Student's t<\/em>-distribution for a homework problem in what follows, including for paired data, you may assume that the underlying population is normally distributed. (When using these tests in a real situation, you must first prove that assumption, however.)<\/p>\r\n\r\n<\/section><\/div>\r\n

            \r\n
            \r\n

            78. The mean number of English courses taken in a two\u2013year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

            \r\n
            \r\n

            79. A student at a four-year college claims that mean enrollment at four\u2013year colleges is higher than at two\u2013year colleges in the United States. Two surveys are conducted. Of the 35 two\u2013year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

            \r\n
            \r\n

            80. At Rachel\u2019s 11th<\/sup> birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Relaxed time (seconds)<\/th>\r\nJumping time (seconds)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            26<\/td>\r\n21<\/td>\r\n<\/tr>\r\n
            47<\/td>\r\n40<\/td>\r\n<\/tr>\r\n
            30<\/td>\r\n28<\/td>\r\n<\/tr>\r\n
            22<\/td>\r\n21<\/td>\r\n<\/tr>\r\n
            23<\/td>\r\n25<\/td>\r\n<\/tr>\r\n
            45<\/td>\r\n43<\/td>\r\n<\/tr>\r\n
            37<\/td>\r\n35<\/td>\r\n<\/tr>\r\n
            29<\/td>\r\n32<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n
            \r\n
            \r\n

            81. Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry-level mechanical engineers and 60 entry-level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

            \r\n
            \r\n

            82. Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the mean number of ring tones for the girls was 3.2 with a standard deviation of 1.5. The mean for the boys was 1.7 with a standard deviation of 0.8. Conduct a hypothesis test to determine if the means are approximately the same or if the girls\u2019 mean is higher than the boys\u2019 mean.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\nUse the information from Appendix C<\/a>\u00a0to answer the next four exercises.<\/em>\r\n

            \r\n
            \r\n

            83. Using the data from Lap 1 only, conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices.<\/p>\r\n\r\n<\/div>\r\n

            84. Repeat the test,\u00a0but use Lap 5 data this time.<\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            85. Repeat the test, but this time combine the data from Laps 1 and 5.<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            86. In two to three complete sentences, explain in detail how you might use Terri Vogel\u2019s data to answer the following question. \u201cDoes Terri Vogel drive faster in races than she does in practices?\u201d<\/span><\/div>\r\n<\/section>\r\n
            <\/div>\r\n
            \r\n
            Use the following information to answer the next two exercises.<\/em> The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals.<\/span><\/div>\r\n<\/section><\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
            Western<\/th>\r\nEastern<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
            Los Angeles 9<\/td>\r\nD.C. United 9<\/td>\r\n<\/tr>\r\n
            FC Dallas 3<\/td>\r\nChicago 8<\/td>\r\n<\/tr>\r\n
            Chivas USA 4<\/td>\r\nColumbus 7<\/td>\r\n<\/tr>\r\n
            Real Salt Lake 3<\/td>\r\nNew England 6<\/td>\r\n<\/tr>\r\n
            Colorado 4<\/td>\r\nMetroStars 5<\/td>\r\n<\/tr>\r\n
            San Jose 4<\/td>\r\nKansas City 3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

            Conduct a hypothesis test to answer the next two exercises.<\/em><\/p>\r\n\r\n

            \r\n
            \r\n

            87. The exact<\/strong> distribution for the hypothesis test is:<\/p>\r\n\r\n

              \r\n \t
            1. the normal distribution<\/li>\r\n \t
            2. the Student's t<\/em>-distribution<\/li>\r\n \t
            3. the uniform distribution<\/li>\r\n \t
            4. the exponential distribution<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
              \r\n
              \r\n

              88. If the level of significance is 0.05, the conclusion is:<\/p>\r\n\r\n

                \r\n \t
              1. There is sufficient evidence to conclude that the W<\/strong> Division teams score fewer goals, on average, than the E<\/strong> teams<\/li>\r\n \t
              2. There is insufficient evidence to conclude that the W<\/strong> Division teams score more goals, on average, than the E<\/strong> teams.<\/li>\r\n \t
              3. There is insufficient evidence to conclude that the W<\/strong> teams score fewer goals, on average, than the E<\/strong> teams score.<\/li>\r\n \t
              4. Unable to determine<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
                \r\n
                \r\n

                89. Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The \u201cday\u201d subscript refers to the statistics day students. The \u201cnight\u201d subscript refers to the statistics night students. A concluding statement is:<\/p>\r\n\r\n

                  \r\n \t
                1. There is sufficient evidence to conclude that statistics night students' mean on Exam 2 is better than the statistics day students' mean on Exam 2.<\/li>\r\n \t
                2. There is insufficient evidence to conclude that the statistics day students' mean on Exam 2 is better than the statistics night students' mean on Exam 2.<\/li>\r\n \t
                3. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.<\/li>\r\n \t
                4. There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section><\/div>\r\n
                  \r\n
                  \r\n

                  90. Elijah wants to know whether textbook costs are different for different courses of study. He selects a random sample of 33 sociology textbooks offered on a popular online site. The mean price of his sample is $74.64 with a standard deviation of $49.36. He then selects a random sample of 33 math and science textbooks from the same site. The mean price of this sample is $111.56 with a standard deviation of $66.90. Is the mean price of a sociology textbook lower than the mean price of a math or science textbook? Test at a 1% significance level.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                  \r\n
                  \r\n

                  91. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                  \r\n
                  \r\n

                  92. Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91, respectively. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The \u201cday\u201d subscript refers to the statistics day students. The \u201cnight\u201d subscript refers to the statistics night students. An appropriate alternative hypothesis for the hypothesis test is:<\/p>\r\n\r\n

                    \r\n \t
                  1. \u03bc<\/em>day<\/sub> > \u03bc<\/em>night<\/sub><\/li>\r\n \t
                  2. \u03bc<\/em>day<\/sub> < \u03bc<\/em>night<\/sub><\/li>\r\n \t
                  3. \u03bc<\/em>day<\/sub> = \u03bc<\/em>night<\/sub><\/li>\r\n \t
                  4. \u03bc<\/em>day<\/sub> \u2260 \u03bc<\/em>night<\/sub><\/li>\r\n<\/ol>\r\n
                    \r\n\r\n \r\n

                    Two Population Means with Known Standard Deviations - Homework<\/h2>\r\n<\/div>\r\n
                    \r\n

                    DIRECTIONS: 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<\/h3>\r\n<\/header>
                    \r\n

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

                    \r\n
                    \r\n

                    93. A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                    \r\n
                    \r\n

                    94. Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n

                    95. A group of transfer-bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $947 and $1,011, respectively. The population standard deviations are known to be $254 and $87, respectively. Conduct a hypothesis test to determine if the means are statistically the same.<\/div>\r\n<\/div>\r\n
                    <\/div>\r\n
                    \r\n
                    96. Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.<\/span><\/div>\r\n<\/div>\r\n
                    <\/div>\r\n
                    \r\n
                    97. A baseball fan wanted to know if there is a difference between the number of games played in a World Series when the American League won the series versus when the National League won the series. From 1922 to 2012, the population standard deviation of games won by the American League was 1.14, and the population standard deviation of games won by the National League was 1.11. Of 19 randomly selected World Series games won by the American League, the mean number of games won was 5.76. The mean number of 17 randomly selected games won by the National League was 5.42. Conduct a hypothesis test.<\/div>\r\n
                    \r\n
                    \r\n

                    98. One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement \u201cI\u2019m pleased with the way we divide the responsibilities for childcare.\u201d The ratings went from one (strongly agree) to five (strongly disagree). The following table<\/a> contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband\u2019s versus the wife\u2019s satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
                    Wife\u2019s Score<\/strong><\/td>\r\n2<\/td>\r\n2<\/td>\r\n3<\/td>\r\n3<\/td>\r\n4<\/td>\r\n2<\/td>\r\n1<\/td>\r\n1<\/td>\r\n2<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
                    Husband\u2019s Score<\/strong><\/td>\r\n2<\/td>\r\n2<\/td>\r\n1<\/td>\r\n3<\/td>\r\n2<\/td>\r\n1<\/td>\r\n1<\/td>\r\n1<\/td>\r\n2<\/td>\r\n4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n
                    \r\n

                    Comparing Two Independent Population Proportions - Homework<\/h2>\r\n
                    \r\n

                    DIRECTIONS: For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in Appendix E.<\/a>\u00a0<\/em><\/p>\r\n\r\n

                    \r\n

                    NOTE<\/h3>\r\n<\/header>
                    \r\n

                    If you are using a Student's t<\/em>-distribution for one of the following homework problems, including for paired data, 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
                    \r\n

                    99. A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n

                    \r\n
                    \r\n

                    100. We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the Whites and the Blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for White females is 4,930. Five hundred eighty were aged 15 to 24. The estimate for Black females is 330. Forty were aged 15 to 24. We will let female suicide victims be our population.<\/p>\r\n101. Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, <\/span>(<\/span>larger\u00a0+\u00a0smaller\u00a0dimension)\/(<\/span><\/span>larger\u00a0dimension<\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 to 1942. Thirty-seven early works were sampled, averaging 1.74 with a standard deviation of 0.11. Sixty-five of the later works were sampled, averaging 1.746 with a standard deviation of 0.1064. Do you think that there is a significant difference in the Golden Ratio calculation?<\/span>\r\n\r\n<\/div>\r\n<\/section>

                    \r\n
                    102. A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?<\/span><\/div>\r\n
                    <\/div>\r\n
                    Use the following information to answer the next three exercises.<\/em> Neuroinvasive West Nile virus is a severe disease that affects a person\u2019s nervous system. It is spread by the Culex species of mosquito. In the United States in 2010, there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test.<\/span><\/div>\r\n<\/section><\/div>\r\n
                    \r\n