A simple random sample of size n is drawn from a population that is normally dis

Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about if the sample size, n, is 29. (b) Construct a 96% confidence interval about if the sample size, n, is 23. (c) Construct a 90% confidence interval about if the sample size, n, is 29. (d) Could we have computed the confidence intervals in parts (a)Hc) if the population had not been normally distributed? Cick the icon to view the table of areas under the t-distribution. (a) Construct a 96% confidence interval about if the sample size, n, is 29. Upper bound: Lower bound (Use ascending order. Round to one decimal place as needed.) (b) Construct a 96% confidence interval about if the sample size, n. is 23. Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E? E? A. B. ° C. As the sample size decreases, the margin of error stays the same. As the sample size decreases, the margin of error decreases. As the sample size decreases, the margin of error increases.

Explanation / Answer

From statistical software outputs,

a) Lower bound = 104

Upper bound = 112

b) Lower bound = 103.4

Upper bound = 112.6

As the sample size decreases, the margin of error increases; Option C

c) Lower bound = 104.8

Upper bound = 111.2

As the percent confidence decreases, the size of the interval decreases; Option C

d) Option B

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