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?

Television A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours.

d. How many people are needed to estimate the number of hours people watch television per week within 2 hours with 90% confidence? Compare this result to part (a). How does decreasing the level of confidence in the estimate affect sample size? Why is this reasonable?

Population A has standard deviation σA = 5, and population B has standard deviation σB = 10. How many times larger than Population A’s sample size does Population B’s need to be to estimate μ with the same margin of error? (Hint: Compute nB/nA.)

Television A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours.

b. How many people are needed to estimate the number of hours people watch television per week within 1 hour with 95% confidence?

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.

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.

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?