TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot." A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.
-Referring to Table 9-7, the null hypothesis will be rejected if the test statistics is
A) greater than 2.3263.
B) less than 2.3263.
C) greater than -2.3263.
D) less than -2.3263.

Question

Quizplus · Accepted Answer

We are testing whether the proportion of viewers who "like the ads a lot" for this brand recognition campaign is less than the typical proportion of 22%. This is a one-tailed test with a significance level of 0.01. Using a z-test, the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)
where:
p = proportion of viewers who "like the ads a lot" for this brand recognition campaign
P = proportion of viewers who "like the ads a lot" for a typical ad (0.22)
n = sample size (1189)

plugging in the numbers, we get:

z = (230/1189 - 0.22) / sqrt(0.22*0.78/1189) = -2.21

Since this is a one-tailed test with the alternative hypothesis being that the proportion for this campaign is less than 22%, we need to find the critical value for a 0.01 level of significance in the t-distribution. Looking at the t-distribution table with degrees of freedom = 1189-1 = 1188 and a one-tailed test at 0.01 level of significance, we find the critical value to be -2.33. Since our calculated z-value (-2.21) is greater than the critical value of -2.33, we fail to reject the null hypothesis. However, we do not reject the alternative hypothesis as we are unable see any evidence of it. Therefore, the choice that satisfies our condition is option D.

TABLE 9-7 A Major Home Improvement Store Conducted Its Biggest Brand Recognition