Question

Also Calculate the test statistic

Also calculate the Confidence interval

STA2023-20Summer B001 Vincent Smith & 07/29/20 8:04 PM Homework: Chapter9 Save Score: 0 of 5 pts 1 3 of 3 (2 complete) HW Score: 50%, 7.5 of 15 pts 9.3.38 Question Help Pair 1 2 The data for a random sample of 8 paired observations are shown in the table to the right. a. What are the appropriate null and alternative hypotheses to test whether the mean for population 2 is larger than that for population 1? b. Conduct the test identified in part a using a=0.10. c. Find a 90% confidence interval for Ho. Interpret this result d. What assumptions are necessary to ensure the validity of this analysis? Population 1 37 33 42 46 3 4 Population 2 39 40 46 51 46 58 49 33 40 6 7 57 42 28 8 a. What are the hypotheses for d = (H1-H2)? A. Ho Hd = 0 OB. Ho Hd > 0 O C. Ho: Hd = 0 Ho Ho < 0 He Hd = 0 He Hd70 OD. Ho Hd = 0 O E. Ho Hd <0 OF. Ho Hd70 Ha Hd > 0 H: Hg = 0 Ha Hd = 0 b. Identify the rejection region for testing the hypotheses from part a. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. t> OB. t OC. t>

Answer 1

	Population 1	Population 2	Difference
	37	39	-2
	33	40	-7
	42	46	-4
	46	51	-5
	40	46	-6
	57	58	-1
	42	49	-7
	28	33	-5
Average	40.625	45.25	-4.625
St. Dev.	8.717	7.815	2.2
n	8	8	8

9) To test. A] Ho! 4d = 0 Hi! 4d co Here X = 40.625, X2= 45.25 S, = 8.717 S₂=7.815 b) Rejection region at < =0.10 dof a7 Cnal) Critical value , te -1.415. Rejection region t < -1.415. OB. tc -1.415. Test Statistics D -4-625 SD 22.2. n=8 D -4.625 E - 5.947 solun 2,2 / 58 ک۱ t 2 t = -5.947 <tc = -1.415. also p-value 0.0003 <o.LO So we reject Ho. conclusion we have ufficient evidence to conclude the claim that mean for population is larger than population 1. Here R=0:10 go y CoI for ud Ď I tcx so [o F = [-2.625 = (-6.099, -3.151) -1.415 X 2.2 ha V8 -6.ogg < Md c-3.151.

Assumptions -

The paired sample t-test has four main assumptions:

• The dependent variable must be continuous (interval/ratio).
• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers.