Question

A simple random sample of 80 items resulted in a sample mean of 60. The population standard deviation is σ = 5.

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 160 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 larger sample size provides a larger margin of error.

A larger sample size provides a smaller margin of error.    

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

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 60

Population standard deviation =    = 5

a) Sample size = n = 80

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

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

= 1.96 * ( 5 /  80 )

= 1.10

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

  ± E

60 ± 1.10

( 58.90, 61.10 )  

b) n = 160
Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 5 /  160 )

= 0.77

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

  ± E

60 ± 0.77

( 59.23, 60.77)  

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