Question

Suppose that you select a sample of size 20 from a single state and find the mean is 31 (Xbar).

a. What is the upper value for the 95% confidence interval for the population mean (mu) for that state. (Assume the standard deviation (sigma) is the same as it is for the entire country (9.25)

b. What is the lower value for the abouve 95% confidence interval for the population mean (mu) for that state is.

Answer 1

Solution :

Given that,

= 31

= .9.25

n = 20

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (9.25 / 20 )

= 4.05

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

- E < < + E

31 - 4.05 < < 31 + 4.05

26.95 < < 35.05

a.)  The   upper value = 35.05

b.)  The lower value = 26.95