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 α = .05 and the following data to test the hypothesis and comment on the value of the commercial Purchase Rating Purchase Rating Individual After Before Individual After Before 4 4 4 a. What are the hypotheses? Ho: 써 is d is less than or less than or equal to 0 Hai d is greater than o b. Compute d (to 3 decimals) 625 Compute sd (to 1 decimal)

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a) Step1: The null and alternative hypotheses are as follows versus

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(b) The computation table After | Before | d= After-Before I d 4 4 The formula for calculating the popul ati on mean difference i:s 1+2-1 2L(4) 0.5 Therefore, the popul ati on mean of the differences is 05 The stan dard deviation of the difference is 12 16 [12-2 (10) V1.428571 = 1 . 195229 s 1.195229 Therefore, the standard deviation of the differences is s1.195229

Step2: Decide the test stati sti c and the level of significance The too5.7 1.895 Step3: State the decision Rule Reject the null hypothesis Ho if t>1.895. Otherwise, we do not reject the null hypothesis Ho Step4: Calculate the value of test stati stic SE- _1.195229 1.195229 2.828427 0.422577 SE = 0.422577 The formula for calculating the test stati stic is SE 0.5 0.422577 1.183216 1.183216 The P- value approach P(t >1.1832) 1- P( s1.1832) = 1-0 862327 0.137673 P-value-0.137673 Step5: Compare with the critical value and make a decision Since, the P- value -0.1376> 0.05. We do not reject the null hypothesis Ho Since, the t-test statistic is t = 1.1832 <605,-1.895. We do not reject the null hypothesis Ho There is not suffi cient evidence to conclude that the m ean difference (i) is greater than zero

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