Question

Given two dependent random samples with the following results:

Population 1	20	22	44	42	28	48	39
Population 2	30	30	32	45	18	43	32

Use this data to find the 99% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Copy Data

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:

Use the 99% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.

Step 4 of 4:

Construct the 99% confidence interval. Round our answers to one decimal places.

Answer 1

Step 1 of 4

x1	x2	d: x2-x1	d-	(d-)2
2020	3030	1010	1197.571429	1434177.326531
2222	3030	808	995.571429	991162.469388
4444	3232	-1212	-1024.428571	1049453.897959
4242	4545	303	490.571429	240660.326531
2828	1818	-1010	-822.428571	676388.755102
4848	4343	-505	-317.428571	100760.897959
3939	3232	-707	-519.428571	269806.040816
		= -1313		= 4762409.7143
		= -1313/7=-187.571429

n : sample size =7

Mean of paired differences :

Step 2 of 4

sample standard deviation of the paired differences :s_d

sample standard deviation of the paired differences :s_d = 890.918039

Step 3 of 4

confidence interval for the true difference between the population means

for 99% confidence level =(100-99)/100 =0.01

/2 = 0.01/2=0.005

degrees of freedom = n-1 =7-1 =6

t_/2,n-1 = t_0.005,6 = 3.7074

99% confidence interval for the true difference between the population means

Step 4 of 4:

99% confidence interval for the true difference between the population means

99% confidence interval for the true difference between the population means = (-1436.0,1060.8)