{"id":5583,"date":"2022-09-27T13:43:12","date_gmt":"2022-09-27T13:43:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5583"},"modified":"2022-09-27T13:43:13","modified_gmt":"2022-09-27T13:43:13","slug":"18c-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/18c-preview\/","title":{"raw":"18C Preview","rendered":"18C Preview"},"content":{"raw":"
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Preparing for the next class<\/div>\r\n
In the next in-class activity, you will need to identify observational units and types of variables, describe how to simulate a random process using a coin, and determine whether data provide evidence against a null hypothesis based on a P-value.<\/div>\r\n
<\/div>\r\n
Questions 1\u20136: After taking several exams in a math course, a student suspects that the majority (more than half) of true\/false questions on exams have a correct answer of \u201cfalse.\u201d To investigate this hypothesis, she takes a sample of 16 true\/false questions from previous exams and determines whether the correct answer for each question is \u201cfalse.\u201d<\/div>\r\n
<\/div>\r\n
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Question 1<\/h3>\r\n
1) What are the observational units in this study?<\/div>\r\n
a) Exams<\/div>\r\n
b) Questions<\/div>\r\n
c) True or false<\/div>\r\n
d) Students<\/div>\r\n<\/div>\r\n<\/div>\r\n
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Question 2<\/h3>\r\n2) What is the sample size?<\/div>\r\n<\/div>\r\n
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Question 3<\/h3>\r\n3) What variable is measured on each observational unit? Is the variable categorical or quantitative?<\/div>\r\n<\/div>\r\n
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Question 4<\/h3>\r\n4) If the two answer options, \u201ctrue\u201d or \u201cfalse,\u201d were equally likely to be the correct answer, how many of the 16 questions would you expect to have \u201cfalse\u201d as the correct answer? Explain.<\/div>\r\n<\/div>\r\n
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Question 5<\/h3>\r\n5) If the two answer options, \u201ctrue\u201d or \u201cfalse,\u201d were equally likely to be the correct answer, describe how you could use a coin to simulate sampling 16 questions and countingthe number of those questions with \u201cfalse\u201d as the correct answer.Clearly explain what each coinfliprepresents, what a \u201cheads\u201d or \u201ctails\u201d outcome would represent, and how you would calculate the sample result.<\/div>\r\n<\/div>\r\n
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Question 6<\/h3>\r\n
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6) Go to the DCMP Sampling Distribution of the Sample Proportiontoolat https:\/\/dcmathpathways.shinyapps.io\/SampDist_prop\/.You will use this toolto simulate the coin-tossing process you described in Question 5.Enter the following inputs:<\/div>\r\n<\/div>\r\n
\r\n
\u2022Set the Population Proportionto0.5. This represents the probability that a coin lands on \u201cheads.\u201d\u2022Set the Sample Sizeto16. This is the number of times we would like to flip the coin.\u2022Under \u201cSelect how many samples you want to simulate drawing from the population,\u201d select \u201c1.\u201d<\/div>\r\n
Part A: Click \u201cDraw Sample(s).\u201d This will generate one sequence of 16coin tossesand plot a bar graph of the results (the Data Distribution), where \u201c1\u201d represents \u201cheads\u201d or a \u201csuccess\u201d and \u201c0\u201d represents \u201ctails\u201d or a \u201cfailure.\u201dIf \u201cheads\u201d represents that the correct answer to a true\/false question is \u201cfalse,\u201d how many questions in this simulation had a \u201cfalse\u201d correct answer?<\/div>\r\n
Hint: The tool displays the number of \u201csuccesses\u201d and the number of \u201cfailures\u201d in the caption of the Data Distribution bar graph.<\/div>\r\n
Part B: Click \u201cReset,\u201d select \u201c1,000\u201dunder\u201cSelect how many samples you want to simulate drawing from the population,\u201d and click \u201cDraw Sample(s).\u201d This will repeat the simulation of sampling 16 true\/false questions 1,000 times. Select \u201cShow Distribution of Successes.\u201d The \u201cSampling Distribution of Number of Successes\u201d shown at the bottom of the page displays how the number of true\/false questions with \u201cfalse\u201d as the correct answer varies across these 1,000 trials of selecting 16 questions. Where is this distribution centered? Does this make sense?Explain.<\/div>\r\n
Part C: In the student\u2019s sample of 16 questions, she found that \u201cfalse\u201d was the correct answer in 11 of the questions. Use the \u201cFind Probability for Samp. Dist.\u201d option in the tool to count the proportion of simulated samples that had 11 or more questions with \u201cfalse\u201d as the correct answer.<\/div>\r\n
Hint: The tool will only calculate the proportion of samples that are at or below a value. Usethetoolto find the proportion of samples that had 10 or fewer questions with \u201cfalse\u201d as the correct answerand then subtract this proportion from 1to obtain your answer.<\/div>\r\n
Part D: Based on your answer in Part C, do you think the student\u2019s data provide evidence that more than half of the true\/false exam questions in this course have \u201cfalse\u201d as the correct answer? Explain how you are using the answer in Part C to determine your answer.<\/div>\r\n
Hint: The value in Part C approximates the P-value for testing the null hypothesis that the two options, \u201ctrue\u201d or \u201cfalse,\u201d are equally likely to be the correct answeron true\/false exam questions in this course.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
Preparing for the next class<\/div>\n
In the next in-class activity, you will need to identify observational units and types of variables, describe how to simulate a random process using a coin, and determine whether data provide evidence against a null hypothesis based on a P-value.<\/div>\n
<\/div>\n
Questions 1\u20136: After taking several exams in a math course, a student suspects that the majority (more than half) of true\/false questions on exams have a correct answer of \u201cfalse.\u201d To investigate this hypothesis, she takes a sample of 16 true\/false questions from previous exams and determines whether the correct answer for each question is \u201cfalse.\u201d<\/div>\n
<\/div>\n
\n
\n

Question 1<\/h3>\n
1) What are the observational units in this study?<\/div>\n
a) Exams<\/div>\n
b) Questions<\/div>\n
c) True or false<\/div>\n
d) Students<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 2<\/h3>\n

2) What is the sample size?<\/p><\/div>\n<\/div>\n

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Question 3<\/h3>\n

3) What variable is measured on each observational unit? Is the variable categorical or quantitative?<\/p><\/div>\n<\/div>\n

\n
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Question 4<\/h3>\n

4) If the two answer options, \u201ctrue\u201d or \u201cfalse,\u201d were equally likely to be the correct answer, how many of the 16 questions would you expect to have \u201cfalse\u201d as the correct answer? Explain.<\/p><\/div>\n<\/div>\n

\n
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Question 5<\/h3>\n

5) If the two answer options, \u201ctrue\u201d or \u201cfalse,\u201d were equally likely to be the correct answer, describe how you could use a coin to simulate sampling 16 questions and countingthe number of those questions with \u201cfalse\u201d as the correct answer.Clearly explain what each coinfliprepresents, what a \u201cheads\u201d or \u201ctails\u201d outcome would represent, and how you would calculate the sample result.<\/p><\/div>\n<\/div>\n

\n
\n

Question 6<\/h3>\n
\n
6) Go to the DCMP Sampling Distribution of the Sample Proportiontoolat https:\/\/dcmathpathways.shinyapps.io\/SampDist_prop\/.You will use this toolto simulate the coin-tossing process you described in Question 5.Enter the following inputs:<\/div>\n<\/div>\n
\n
\u2022Set the Population Proportionto0.5. This represents the probability that a coin lands on \u201cheads.\u201d\u2022Set the Sample Sizeto16. This is the number of times we would like to flip the coin.\u2022Under \u201cSelect how many samples you want to simulate drawing from the population,\u201d select \u201c1.\u201d<\/div>\n
Part A: Click \u201cDraw Sample(s).\u201d This will generate one sequence of 16coin tossesand plot a bar graph of the results (the Data Distribution), where \u201c1\u201d represents \u201cheads\u201d or a \u201csuccess\u201d and \u201c0\u201d represents \u201ctails\u201d or a \u201cfailure.\u201dIf \u201cheads\u201d represents that the correct answer to a true\/false question is \u201cfalse,\u201d how many questions in this simulation had a \u201cfalse\u201d correct answer?<\/div>\n
Hint: The tool displays the number of \u201csuccesses\u201d and the number of \u201cfailures\u201d in the caption of the Data Distribution bar graph.<\/div>\n
Part B: Click \u201cReset,\u201d select \u201c1,000\u201dunder\u201cSelect how many samples you want to simulate drawing from the population,\u201d and click \u201cDraw Sample(s).\u201d This will repeat the simulation of sampling 16 true\/false questions 1,000 times. Select \u201cShow Distribution of Successes.\u201d The \u201cSampling Distribution of Number of Successes\u201d shown at the bottom of the page displays how the number of true\/false questions with \u201cfalse\u201d as the correct answer varies across these 1,000 trials of selecting 16 questions. Where is this distribution centered? Does this make sense?Explain.<\/div>\n
Part C: In the student\u2019s sample of 16 questions, she found that \u201cfalse\u201d was the correct answer in 11 of the questions. Use the \u201cFind Probability for Samp. Dist.\u201d option in the tool to count the proportion of simulated samples that had 11 or more questions with \u201cfalse\u201d as the correct answer.<\/div>\n
Hint: The tool will only calculate the proportion of samples that are at or below a value. Usethetoolto find the proportion of samples that had 10 or fewer questions with \u201cfalse\u201d as the correct answerand then subtract this proportion from 1to obtain your answer.<\/div>\n
Part D: Based on your answer in Part C, do you think the student\u2019s data provide evidence that more than half of the true\/false exam questions in this course have \u201cfalse\u201d as the correct answer? Explain how you are using the answer in Part C to determine your answer.<\/div>\n
Hint: The value in Part C approximates the P-value for testing the null hypothesis that the two options, \u201ctrue\u201d or \u201cfalse,\u201d are equally likely to be the correct answeron true\/false exam questions in this course.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":68,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5583","chapter","type-chapter","status-publish","hentry"],"part":5563,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5583\/revisions"}],"predecessor-version":[{"id":5584,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5583\/revisions\/5584"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5563"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5583\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5583"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5583"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5583"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}