Question

A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use a = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. Purchase Rating Individual After Before State the null and alternative hypotheses. (Use ud - mean rating after - mean rating before.) Houd = 0 Ha: d + 0 HOUSO Ha: Hd > 0 Ho: Md 30 Ha: “d = 0 Ho: Md0 | Ha: Id = 0 Houd > 0 Hai Hd SO Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value State your conclusion. Do not Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. Do not reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. Reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

Answer 1

	X	Y	d	d-d̅	(d-d̅)2
	6	5	1	0.5	0.25
	6	4	2	1.5	2.25
	7	8	-1	-1.5	2.25
	4	3	1	0.5	0.25
	3	5	-2	-2.5	6.25
	9	8	1	0.5	0.25
	7	5	2	1.5	2.25
	6	6	0	-0.5	0.25
Total			4		14
		d̅=mean	Total/8
		d̅=	0.5

x : purchase rating (ARH Y : Purchase rating (Before d = x -Y lld i mean nating after - mean nating before The null hypothesis stated that the mean rating "afte could be less than or equal to the mean rating ibor Ho ld co ۵< اے لد :Ha J = {di = 4 TD0.5 8- 15d = 1.41 test statistic teau = 7 - Salon tay -0.5 1.41158 1.41/2.83 teay = 1 P value = P('tn-l tool) = P(E81 > 1) - P (tz > 1) on and nopea ca =x-P (tz (1) 1 - 0.8413 = 0.1587 IP value

Decision Here we Reject Ho if P valve P value = 0.1587 fail to reject Ho ca 2=0.05 > conclusion Do not reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase