Question

A simple random sample of size nis drawn from a population that is normally distributed. The sample mean, X, is found to be 106, and the sample standard deviations, is found to be 9. (a) Construct a 95% confidence interval about if the sample size, n, is 26 (b) Construct a 95% confidence interval about if the sample size, n, is 13 (c) Construct a 90% confidence interval about if the sample size, n, is 26 (d) Should the confidence intervals in parts ( c) have been computed if the population had not been normally distributed? (a) Construct a 95% confidence interval about if the sample size, n, is 26 Lower bound: Upper bound: (Round to one decimal place a nended.) (b) Construct a 96% confidence interval about if the sample size, n, is 13. Lower bound: Upper bound: (Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E? O A. As the sample so decreases, the margin of error stays the same O B. As the sample size decreases, the margin of error decreases OC. As the sample size decreases the margin of error increases. (c) Construct a 90% confidence interval about it the sample size is 26 Lower bound: Upper bound: (Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? O A. As the level of confidence decreases the size of the interval decreases

Answer 1

c) Given, X=106, 5=9 n=26 90% confidence interval for u Lower bound= x-tn-1,9 s =106-1.7056 * g Vzo 106- 3.0105 Lower bound= 103.0 Upper bound= 8+ tn-1,* = 100+ 3.0105 Upper bound - log.o compare the results to those obtained in part (a) How does decreasing the level of confidence affect the size of the margin Error E? As the level of confidence decreases, the size of interval decreuses.

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