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. [You may find it useful to reference the t table.]

a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to at least 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.)

b. Construct the 95% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

c. Construct the 99% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)

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

• As the confidence level increases, the margin of error becomes smaller.

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

Answer 1

The statistical software output for this problem is:

Hence,

a) Sample mean = 18.75

Sample standard deviation = 6.86

b) 95% confidence interval: 13.01 to 24.49

c) 99% confidence interval: 10.26 to 27.24

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