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.

True or False: The distribution of the sample mean, x̄, will be approximately normally distributed if the sample is obtained from a population that is not normally distributed, regardless of the sample size.

A simple random sample of size n = 20 is obtained from a population with μ = 64 and σ = 17.

d. Compare the results obtained in parts (b) and (c) with the results obtained in parts (b) and (c) in Problem 17. What effect does increasing the sample size have on the probabilities? Why do you think this is the case?

Upper Leg Length The upper leg length of 20- to 29-year-old males is approximately normal with a mean length of 43.7 cm and a standard deviation of 4.2 cm.

Source: “Anthropometric Reference Data for Children and Adults: U.S. Population, 1999–2002”; Volume 361, July 7, 2005.

d. What effect does increasing the sample size have on the probability? Provide an explanation for this result.

Old Faithful The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is approximately normal with standard deviation 21.25 minutes, answer the following questions: Source: www.unmuseum.org

c. What effect does increasing the sample size have on the probability? Provide an explanation for this result.

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?

[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?