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 35 business​ days, the mean closing price of a certain stock was ​$109.47. Assume the population standard deviation is ​$10.14. please answer both questions, thank you

Answer 1

Solution :

Given that,

= 109.47.

=10.14

n = 35

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 * (10.14 / 35 )

= 2.82

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

- E < < + E

109.47 - 2.82 < < 109.47.+ 2.82

106.65 < < 112.29

b ) 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 * (10.14 / 35 )

= 3.36

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

- E < < + E

109.47. - 3.36 < < 109.47.+ 3.36

106.11 < < 112.83