Question

Given two dependent random samples with the following results:

Population 1 32 35 45 46 43 45 30

Population 2 19 40 31 32 30 47 42

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 98% confidence interval. Round your answers to one decimal place.

Answer 1

Number	Population 2	Population 1	Difference
	19	32	-13	64
	40	35	5	100
	31	45	-14	81
	32	46	-14	81
	30	43	-13	64
	47	45	2	49
	42	30	12	289
Total	241	276	-35	728

For 90% confidence interval

Step 1

Point Estimate

Step 2

Step 3

Margin of Error =

Step 4

Confidence Interval :-

t_{\alpha /2} = t_{ 0.1 /2} = 1.943

Lower Limit =
Lower Limit = -13.0899 ≈ -13.1
Upper Limit =
Upper Limit = 3.0899 ≈ 3.1
90% Confidence interval is ( -13.1 , 3.1 )

For 98% confidence interval

Step 3

Margin of Error =

Step 4

Confidence Interval :-



Lower Limit =
Lower Limit = -18.0836 ≈ -18.1
Upper Limit =
Upper Limit = 8.0836 ≈ 8.1
98% Confidence interval is ( -18.1 , 8.1 )