Question

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is

σ = 15.

(a)

Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)

( )to( )

(b)

Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)

( )to( )

(c)

What is the effect of a larger sample size on the interval estimate?

A. A larger sample size does not change the margin of error.

B. A larger sample size provides a smaller margin of error.    

C. A larger sample size provides a larger margin of error.

Answer 1

Solution:

Given: A simple random sample of 60 items resulted in a sample mean of 90.

The population standard deviation is σ = 15.

= 90

n = 60

Part a) Compute the 95% confidence interval for the population mean.

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus

Part b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean.

n = 120

Thus

Part c) What is the effect of a larger sample size on the interval estimate?

B. A larger sample size provides a smaller margin of error.