In a survey of introductory statistics students, an instructor asked her student
ID: 3053242 • Letter: I
Question
In a survey of introductory statistics students, an instructor asked her students how many flip-flops they have. Suppose that the intent is to study whether there is an association between number of flip-flops and a person’s sex.
1. Identify the explanatory and response variables. Also, for each variable identify whether it is categorical or quantitative.
2. Which of the following is the appropriate null hypothesis?
3. Which of the following is the appropriate alternative hypothesis?
Here are a few summary statistics about the data:
4. In this context, which of the following is an (are) appropriate statistic value(s) to compare men to women? Check all that apply.
5. Suppose that we want to use cards to carry out a randomization test of the appropriate hypotheses. How many cards will we need?
6. Find a standardized statistic to test whether the average number of flip-flops men have is different from that of women. Report the standardized statistic in the context of the study. Use the table and graph provided. Round to two decimal places.
The p-value for the randomization-based test of whether the average number of flip-flops men have is different from that of women turns out to be 0.001.
7.
Interpret this p-value in the context of the study.
a. The probability of not obtaining a difference in the average number of flip-flops for men and women of 3.68 or larger or –3.68 or smaller by chance (if the null is true) is approximately 0.001.
b. The probability of a man having more flip-flips than a woman.
c. The probability of a woman having more flip-flips than a man.
d. The probability of obtaining a difference in the average number of flip-flops for men and women of 3.68 or larger or –3.68 or smaller by chance (if the null is true) is approximately 0.001.
8. ?Use the 2SD method and the information available in the previous exercises to find a 95% confidence interval for the difference in average number of flip-flops that men have and that women have. Round to two decimal places.
9. Interpret the confidence interval reported in part (a) in the context of the study.
a. We are 95% sure that females own between 1.25 and 6.11 fewer flip-flops on average than males in the population.
b. We are 95% sure that males own between 1.25 and 6.11 fewer flip-flops on average than females in the population.
c. We are 95% sure that females own between 1.25 and 6.11 more flip-flops on average than males in the population.
d. We are 95% sure that males own between 1.25 and 6.11 more flip-flops on average than females in the population.
a. On average, men have more flip-flops than women. SampleSampleSample Sample size 37 13 mean median 6.22 2.54 SD 3.58 2.96 Women 6.00 1.00 MenExplanation / Answer
1) Explanatory variables = no.of flip flops (quantitative variable)
Response variable = sex ( is categorical variable)
2) Ho : There is no association between a person’s sex and the number of flip-flops that they own
3) Ha : There is an association between a person’s sex and the number of flip-flops that they own.
4) Appropriate test statistic = 6.22 - 2.54 = 3.68 & 3.58 - 2.96 = 0.62
5) 50 i.e. (37+13 = 50)
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