Question

A sample of 25 observations is selected from a normal population where the population standard deviation is 32. The sample mean is 77.  

a. Determine the standard error of the mean. (Round the final answer to 3 decimal places.)

The standard error of the mean is .

b. Determine the 95% confidence interval for the population mean. (Round the z-value to 2 decimal places. Round the final answers to 3 decimal places.)

The 95% confidence interval for the population mean is between and .

c. If you wanted a wider interval, would you increase or decrease the confidence level?

Answer 1

Sample size, n = 25

Mean, = 77

Standard deviation, = 32

a) Standard error =

= 32/5

= 6.4

b) Confidence interval = Z*

For 95% confidence level, Z* = 1.96

Confidence interval = 77 1.96 x 6.4

= (​​​​​64.456, 89.544)

c) as confidence level increases, z* value increases. With increase in z value, the interval gets wider

So, if you want a wider interval, you have to increase the confidence level