Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, is found to be

114 and the sample standard​ deviation, s, is found to be 10

1. Construct a 95% confidence interval about the mean if the sample​ size, n, is 28

​2. Construct a 95% confidence interval about the mean if the sample​ size, n, is 13

​3. Construct an 80% confidence interval about the mean if the sample​ size, n, is 28

​4. Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

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?

A. As the level of confidence decreases, the size of the interval stays the same.

B. As the level of confidence decreases, the size of the interval decreases

C. As the level of confidence decreases the size of the interval increases

​(d) Could we have computed the confidence intervals in parts​ (1)-(3) if the population had not been normally​ distributed?

A. No, the population does not need to be normally distributed.

B. Yes, the population needs to be normally distributed.

C. Yes, the population does not need to be normally distributed.

D. No, the population needs to be normally distributed.

Answer 1

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