Question

1.

A. In a random sample of 40 games, the home team won 23 games and lost 17 games. Use StatKey to construct a 95% bootstrap confidence interval using the percentile method to estimate the proportion of all games won by the home team in the population. Take at least 5,000 resamples.

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

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

D. Using the dataset with 230 out of 400 matches won, construct a 99% confidence interval in StatKey using the percentile method. Take at least 5,000 resamples.

Answer 1

(a) The Statkey output is:

The 95% bootstrap confidence interval using the percentile method to estimate the proportion of all games won by the home team in the population is between 0.4482 and 0.7518.

(b) Since the confidence interval contains 0.5, we cannot conclude that the proportion of games won by the home team is different from 0.50.

(c) As the sample size increases, the width of the confidence interval decreases.

(d) The Statkey output is:

The 99% bootstrap confidence interval using the percentile method is between 0.5652 and 0.6898.