Question

# A market research firm used a sample of individuals to rate the purchase potential of a...

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 α = 0.05 and the following data to test the hypothesis and comment on the value of the commercial.

Individual Purchase Rating
After Before
1 6 5
2 6 4
3 7 7
4 4 3
5 3 6
6 9 8
7 7 5
8 6 7

1. State the null and alternative hypotheses. (Use μd = mean rating after − mean rating before.

2. Calculate the value of the test statistic. (Round your answer to three decimal places.)

3. Calculate the p-value. (Round your answer to four decimal places.)

4. State your conclusion.

a) Do not reject H0. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. b) Do not Reject H0. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. c) Reject H0. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. d)Reject H0. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

1) Ho: ≤ 0

Ha: > 0

2) Test statistics

 employee After Before Diff (Aft-Bef) Dev (diff - mean) Sq deviation 1 6 5 1 0.63 0.39 2 6 4 2 1.63 2.64 3 7 7 0 -0.38 0.14 4 4 3 1 0.63 0.39 5 3 6 -3 -3.38 11.39 6 9 8 1 0.63 0.39 7 7 5 2 1.63 2.64 8 6 7 -1 -1.38 1.89 Total 48 45 3 0.0000 19.8750

= 3/ 8 = 0.375

t stat = 0.629

(3) p value = TDIST (0.629, 7,1) = 0.2745

(4) p value is > 0.05, hence fail to reject Ho.

a) Do not reject H0. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.

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