Question

A simple random sample of 60 items results in a sample mean of 80. The population standard deviation is σ = 15.

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

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

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 80

Population standard deviation =    = 15

Sample size = n = 60

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 * (15 /  60 )

= 3.80

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

  ± E

80 ± 3.80   

( 76.20, 83.80 )

b) n = 120

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

= 1.96 * ( 15 /  120 )

= 2.68

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

  ± E

   80 ± 2.68   

( 77.32, 82.68 )