Question

11. A random sample of 22 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 135.5 and 30.50, respectively. Assume that the population is normally distributed. [You may find it useful to reference the t table.]

a. Construct the 90% confidence interval for the population mean.

(Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Confidence Interval

? (124.80 WRONG)

to

? (146.20 WRONG)

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

(Round intermediate calculations to at least 4 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

Confidence Interval

? (118.75 WRONG)

to

? (152.25 WRONG)

c. Use your answers to discuss the impact of the confidence level on the width of the interval.

1. As the confidence level increases, the interval becomes wider.

2. As the confidence level increases, the interval becomes narrower.

Please do not answer if you are not sure, THANk YOU! :)

Answer 1

The statistical software output for this problem is:

Hence,

a) 90% confidence interval:

124.31 to 146.69

b) 99% confidence interval:

117.09 to 153.91

c) As the confidence level increases, the interval becomes wider.