Question

A simple random sample of 70 items resulted in a sample mean of 60. 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 140 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 provides a larger margin of error.

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

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

Answer 1

Solution :

Given that,

a) Z/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 15 /  70 )

= 3.51

At 95% confidence interval estimate of the population mean is,

  ± E   

= 60 ± 3.51

= ( 56.49, 63.51 )

b) Z/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 15 /  140 )

= 2.48

At 95% confidence interval estimate of the population mean is,

  ± E   

= 60 ± 2.48

= ( 57.52, 62.48 )

c) C. A larger sample size provides a smaller margin of error.