Question

4. A market research company wants to assess the potential for purchasing a new product "before" and "after" an individual sees a television advertisement about that product. The ranking of potential purchases is based on a scale of 0 to 10, with a higher value indicating a higher purchase potential. The null hypothesis states that the average rating of "After" will be less than or equal to the average value of "before." A rejection of this hypothesis will show that advertising increases the average potential buying rank. Use α = 0.05 and the following data to test the hypothesis.

Individual	Purchase Rating
	after	before
1	6	5
2	6	4
3	7	7
4	4	3
5	3	5
6	9	8
7	7	5
8	6	6

Answer 1

Solution:-

uBefore - uAfter = uD

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis

Null hypothesis: ud = 0

Alternative hypothesis: uD > 0

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).

s = 1.8468

SE = s / sqrt(n)

S.E = 0.6529

DF = n - 1 = 8 -1

D.F = 7

t = [ (x1 - x2) - D ] / SE

t = 0.9573

where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.

Since we have a one-tailed test, the P-value is the probability that a t statistic having 7 degrees of freedom is greater than 0.9573.

Thus, the P-value = 0.185.

Interpret results. Since the P-value (0.185) is greater than the significance level (0.05), hence we failed to reject the null hypothesis.

Do not reject H0.

From the above test we do not have sufficient evidence in the favor of the claim that the average rating of "After" will be less than or equal to the average value of "before." .