statistics

Sections 4.2 to 4.3 MATH 1342 Page 1 of 2

Due: _________________ Name:

Elementary Statistics Take-Home Quiz 8 Sections 4.2-4.3

Textbook problems to be completed on separate paper and turned in with this quiz are after Sections 4.2 & 4.3. Write all hypotheses using both words and symbols. There is no need to turn in StatKey output for these textbook problems.

4.55 4.71 4.93 4.107 4.115

Software output is required for this assignment.

1. 4.72 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 data are in Brain Size (Football: No Concussion vs Concussion) where the variable Hipp measures brain size as the volume of the hippocampus (in μL) for each subject. 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, using words and symbols.

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(s) with your quiz submission and write the p-value here.

𝑝 − 𝑣𝑎𝑙𝑢𝑒 =____________

e. Write a “strength of evidence” conclusion for the test in context.

Sections 4.2 to 4.3 MATH 1342 Page 2 of 2

2. 4.114 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, using words and symbols.

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(s) with your quiz submission, and write the p-value here.

𝑝 − 𝑣𝑎𝑙𝑢𝑒 =____________

e. At the a = 0.1 level, what is the formal statistical decision of this test (Reject / Fail to reject 𝐻 )?

__________________________________________________

f. Write a statistical significance conclusion for the test in context.