Asimple 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?

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.