[DATA] Effect of Outliers The following small data set represents a simple random sample from a population whose mean is 50.
e. Compute a 95% confidence interval for the large data set. Compare the results to part (a). What effect does increasing the sample size have on the confidence interval?

Sampling Distributions The following data represent the running lengths (in minutes) of the winners of the Academy Award for Best Picture for the years 2012–2017.

f. Repeat parts (b)–(e) using samples of size n=3. Comment on the effect of increasing the sample size.

Threaded Problem: Tornado The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017.

c. Based on the shape of the distribution of the variable “Length” from the histogram in part (a), what must be true about the sample size in order for the distribution of the sample mean to be approximately normal?

[NW] Determining Sample Size A physical therapist wants to determine the difference in the proportion of men and women who participate in regular, sustained physical activity. What sample size should be obtained if she wishes the estimate to be within 3 percentage points with 95% confidence, assuming that

a. she uses the 1998 estimates of 21.9% male and 19.7% female from the U.S. National Center for Chronic Disease Prevention and Health Promotion?

Determining Sample Size An educator wants to determine the difference between the proportion of males and females who have completed four or more years of college. What sample size should be obtained if she wishes the estimate to be within 2 percentage points with 90% confidence, assuming that

a. she uses the 1999 estimates of 27.5% male and 23.1% female from the U.S. Census Bureau?

A puzzle company is interested in the average number of pieces in their jigsaw puzzles, so they plan to create a confidence interval for the true mean. The easiest puzzle in their line is $100$ pieces, and the largest is $1000$ pieces. Use the range rule of thumb to estimate the sample standard deviation.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(A) The standard deviation is known to be about $96$ pages.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(B) The standard deviation is unknown, but the longest book is $697$ pages and the shortest is $298$ pages.

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 108, and the sample standard deviation, s, is found to be 10.

b. Construct a 96% confidence interval for μ if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E?