Question

A simple random sample of size n is drawn from a population that is normally distributed with population standard deviation of 13 (σ =13). The sample mean is 108 (?̅= 108). Compute a 96 percent confidence interval for the population mean (μ) for a sample size of 25 (n = 25).

a. Will you use a z value or a t value in your calculation? Explain?

b. What is the value of z or t that you will use in your calculation? ___________

c. What is the margin of error.

d. Compute the 96% confidence interval for the population mean (μ) for a sample size of 25 (n = 25).

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 108

Population standard deviation =    = 13

Sample size = n = 25

a) we use z distribution, because population standard deviation is known.

b) At 96% confidence level

= 1 - 96%  

= 1 - 0.96 =0.04

/2 = 0.02

Z/2 = Z_0.02 = 2.054

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

= 2.054 * ( 13 /   25)

= 5.34

d) At 96% confidence interval estimate of the population mean is,

  ± E

108 ± 5.34

(102.66, 113.34)