Question

A simple random sample of 70 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.)

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.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 90  

Population standard deviation = = 15

A) Sample size = n = 70

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960

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

=1.960 * (15 /70 )

= 3.51

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

- E < < + E

90 -3.51 <   < 90+ 3.51

86.49<   <93.51

(86.49 ,93.51 )

B)

Sample size = n = 140

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z0.025 = 1.960

Z/2 = 1.960

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

=1.960 * (15 /140 )

=2.48

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

- E < < + E

90 -2.48<   < 90+ 2.48

86.49<   <93.51

(87.52 ,92.48 )