1. Concussions and Brain Size. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The variable Hipp measures brain size as the volume of the hippocampus (in μL) for each subject. Uploading the file FootballBrain is not recommended for this problem. You can find the data in the drop-down menu, as Brain Size (Football:No Concussion vs. Concussion). a. Define the parameter(s) for this question, using appropriate notation. b. Write the null and alternative hypotheses in terms of the parameter(s) above. c. Use StatKey to find the value of the relevant sample statistic. Write it using correct notation. d. Use StatKey to find the p-value for your hypotheses. Include a screenshot of the randomization dotplot with tail area with your homework submission, and write the p-value here. e. State the conclusion of the test in context, using nontechnical language. Include wording to indicate the strength of the evidence against H0. f. Assuming there is a significant difference, can we conclude from this study that concussions cause the differences we see in brain size? Justify your answer based on the methodology of the study. 2. The Ignorance Survey: United Kingdom. Exercise 4.113 refers to a survey used to assess the ignorance of the public to global population trends. A similar survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked, “In the last 20 years the proportion of the world population living in extreme poverty has …,” and three choices were provided: 1)“increased” 2) “remained more or less the same,” and 3) “decreased.” Of 373 university degree holders, 45 responded with the correct answer: decreased; of 639 non-degree respondents, 57 responded with the correct answer. We would like to test if the percent of correct answers is significantly different between degree holders and non-degree holders. a. Define the parameter(s), using appropriate notation. b. Write the null and alternative hypotheses in terms of the parameter(s) above. c. Use StatKey to find the value of the relevant sample statistic. Write it using correct notation. d. Using StatKey, construct a randomization distribution and compute the p-value. Include a screenshot of the randomization dotplot with tail area with your homework submission, and write the p-value here. Remember that counts can be entered manually for categorical data, and you do not need a dataset. Click on Edit Data. e. At the level, what is the formal statistical decision of this test (Reject H0 / Fail to reject H0)? f. State the conclusion in context, using nontechnical language.
1. Concussions and Brain Size. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The variable Hipp measures brain size as the volume of the hippocampus (in μL) for each subject. Uploading the file FootballBrain is not recommended for this problem. You can find the data in the drop-down menu, as Brain Size (Football:No Concussion vs. Concussion). a. Define the parameter(s) for this question, using appropriate notation. b. Write the null and alternative hypotheses in terms of the parameter(s) above. c. Use StatKey to find the value of the relevant sample statistic. Write it using correct notation. d. Use StatKey to find the p-value for your hypotheses. Include a screenshot of the randomization dotplot with tail area with your homework submission, and write the p-value here. e. State the conclusion of the test in context, using nontechnical language. Include wording to indicate the strength of the evidence against H0. f. Assuming there is a significant difference, can we conclude from this study that concussions cause the differences we see in brain size? Justify your answer based on the methodology of the study.
2. The Ignorance Survey: United Kingdom. Exercise 4.113 refers to a survey used to assess the ignorance of the public to global population trends. A similar survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked, “In the last 20 years the proportion of the world population living in extreme poverty has …,” and three choices were provided: 1)“increased” 2) “remained more or less the same,” and 3) “decreased.” Of 373 university degree holders, 45 responded with the correct answer: decreased; of 639 non-degree respondents, 57 responded with the correct answer. We would like to test if the percent of correct answers is significantly different between degree holders and non-degree holders. a. Define the parameter(s), using appropriate notation. b. Write the null and alternative hypotheses in terms of the parameter(s) above. c. Use StatKey to find the value of the relevant sample statistic. Write it using correct notation. d. Using StatKey, construct a randomization distribution and compute the p-value. Include a screenshot of the randomization dotplot with tail area with your homework submission, and write the p-value here. Remember that counts can be entered manually for categorical data, and you do not need a dataset. Click on Edit Data. e. At the level, what is the formal statistical decision of this test (Reject H0 / Fail to reject H0)? f. State the conclusion in context, using nontechnical language.
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