Question

The random sample shown below was selected from a normal distribution.

5,5,3,10,10,3

a. Construct a 99% confidence interval for the population mean mu. ( , ) (Round to two decimal places as needed.)

b. Assume that sample mean and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n = 25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence intervals? The confidence interval is ( ). (Round to two decimal places as needed.)

What is the effect of the sample size on the width of the confidence interval?

As the sample size increases, the width decreases.

As the sample size increases, the width increases.

As the sample size increases, the width stays the same.

Answer 1

	Values ( X )
	5	1
	5	1
	3	9
	10	16
	10	16
	3	9
Total	36	52

Mean

Standard deviation

Part a)

Confidence Interval



Lower Limit =
Lower Limit = 0.6914
Upper Limit =
Upper Limit = 11.3086
99% Confidence interval is ( 0.69 , 11.31 )

Margin of Error =

Width = 11.31 - 0.69 = 10.62

Part b)

Confidence Interval



Lower Limit =
Lower Limit = 4.196
Upper Limit =
Upper Limit = 7.804
99% Confidence interval is ( 4.20 , 7.80 )

Margin of Error =

Width = 7.80 - 4.20 = 3.61

As the sample size increases, the width decreases.