## A simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. a. Develop a 90% confid

Question

A simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.

a. Develop a 90% confidence interval for the population mean.

b. Develop a 95% confidence interval for the population mean.

c. Develop a 99% confidence interval for the population mean.

d. What happens to the margin of error and the confidence interval as the confidence level is increased?

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3 days 2021-10-10T23:55:41+00:00 1 Answer 0

When confidence level increases, margin of error increases thus making confidence interval wider.

Step-by-step explanation:

Given that a simple random sample with n=54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.

Since n >30 but population std deviation is not known we can use only t critical value.

a) t critical = 2.006

Hence 90% confidence interval = Mean ± = b) t critical = 2.30687 = 2.31

Hence 90% confidence interval = Mean ± = c) t critical = 2.30687 = 2.31

Hence 90% confidence interval = Mean ± = d) When confidence level increases, margin of error increases thus making confidence interval wider.