Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of 48 business​ days, the mean closing price of a certain stock was ​$106.06. Assume the population standard deviation is ​$11.45.

The​ 90% confidence interval is ( [ ], [ ] ).

Answer 1

Solution

Given that,

= 106.06

= 11.45

n = 48

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z 0.05 = 1.645

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

= 1.645* (11.45 / 48 )

= 2.72

At 90% confidence interval estimate of the population mean is,

- E < < + E

106.06 - 2.72 < < 106.06 + 2.72

103.34 < < 106.78

(103.34 , 106.78)

b ) At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960* (11.45 / 48 )

= 3.24

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

- E < < + E

106.06 - 3.24< < 106.06 + 3.24

102.82 < < 109.30

(102.82, 109.30)