Question

A simple random sample of 60 items resulted in a sample mean of 69. The population standard deviation is 17.

a. Compute the 95% confidence interval for the population mean (to 1 decimal).

( , )

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).

( , )

c. What is the effect of a larger sample size on the margin of error?

- it increases, it decreases, it stays the same, or it cannot be determined from the given data??

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 69

Population standard deviation =    = 17

Sample size = n = 60

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 17/  60 )

= 4.3

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

  ± E

69 ± 4.3

( 64.7 , 73.3)

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

= 1.96 * ( 17/  120 )

= 3.04

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

  ± E

69 ± 3.04

( 65.96 , 72.04)

c. the effect of a larger sample size on the margin of error

it decreases,