What if the sample size were 10 times bigger

Reference no: EM132464095

Directions

· Answer the questions in this document in a different color and not bolded.

· Always show your work and clearly identify your final answer. Full credit will not be given to answers without work shown. If you do hand calculations, show your work using Word's equation editor.

· When you use StatKey, include all relevant output and clearly identify your final answer by writing a sentence.

· Round all answers to 3 decimal places unless otherwise specified.

· If you have any questions, post them to the course discussion board.

· StatKey needed: https://www.lock5stat.com/StatKey/

1. The following questions are related to the proportion of Major League Soccer (MLS) matches won by the home team.

A. In a random sample of 22 MLS matches, the home team won 13 of those matches. Use StatKey to construct a 95% bootstrap confidence interval using the percentile method. Take at least 5,000 resamples. Don't forget to include a screenshot from StatKey and to identify your answer.

B. Interpret the meaning of the confidence interval constructed in part A by completing the phrase below.

I am 95% confident...

C. Given your confidence interval in part A, is there evidence that in the population, the proportion of matches won by the home team is different from 0.50 (i.e., half)? Explain why or why not.

D. What if the sample size were 10 times bigger? Find the confidence interval if we had a sample where 130 out of 220 matches were won by the home team. Use StatKey to construct a 95% confidence interval using the percentile method with these new data (x=130, n=220). Take at least 5,000 resamples. Don't forget to include a screenshot from StatKey and to identify your answer.

E. When the sample size was increased, how did the confidence interval change? Explain why.

F. Using the dataset with 130 out of 250 matches won, construct a 99% confidence interval in StatKey using the percentile method. Take at least 5,000 resamples. Don't forget to include a screenshot from StatKey and to identify your answer.

G. When the confidence level was changed from 95% to 99%, how did the confidence interval change? Explain why.

2. For the following questions you will use StatKey to construct bootstrap confidence intervals for the difference in two means. Use the "Exercise Hours (Male-Female)" dataset built into StatKey to address the following.

A. Using the percentile method, construct a 95% confidence interval for the difference in the mean hours per week spent exercising for males and females. Take at least 5,000 resamples. Don't forget to include a screenshot from StatKey and to identify your answer.

B. Using the standard error method, construct a 95% confidence interval for the difference in the mean hours per week spent exercising for males and females. You can use the standard error from the bootstrap distribution you constructed in part A. Show all of your work using the equation editor.

C. Explain why the confidence intervals you constructed using the percentile method and the standard error method are not exactly the same. In other words, why may we expect answers in parts A and B to be slightly different?

Reference no: EM132464095

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