Question

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 16, 26, 20, 14, 23, 10, 12, 29.

A. Calculate the sample mean and the sample standard deviation.

Sample mean:

Sample standard deviation:

B. Construct the 95% confidence interval for the population mean.

Confidence interval ______ to ______

C. Construct the 99% confidence interval for the population mean.

Confidence interval ______ to ______

D. What happens to the margin of error as the confidence level increases from 95% to 99%?

(multiple choice)

-As the confidence level increases, the margin of error becomes smaller

or

-As the confidence level increases, the margin of error becomes larger

Answer 1

a) = (16 + 26 + 20 + 14 + 23 + 10 + 12 + 29)/8 = 18.75

b) s = sqrt(((16 - 18.75)^2 + (26 - 18.75)^2 + (20 - 18.75)^2 + (14 - 18.75)^2 + (23 - 18.75)^2 + (10 - 18.75)^2 + (12 - 18.75)^2 + (29 - 18.75)^2)/7) = 6.861

c) At 95% confidence interval the critical value is t^* = 2.365

The 95% confidence interval for population mean is

+/- t^* * s/

= 18.75 +/- 2.365 * 6.861/

= 18.75 +/- 5.74

= 13.01, 24.49

d) At 99% confidence interval the critical value is t^* = 3.5

The 99% confidence interval for population mean is

+/- t^* * s/

= 18.75 +/- 3.5 * 6.861/

= 18.75 +/- 8.49

= 10.26, 27.24

D) As the confidence level increases, the margin of error becomes larger.