SCENARIO 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 Scenario 9-7,the null hypothesis will be rejected if the test statistic 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

Since we want to test if the series of television advertisements is less successful than the typical ad, we are interested in a one-tailed test with the alternative hypothesis being that the proportion of viewers who "like the ads a lot" is less than 22%. To conduct the hypothesis test, we can use the one-sample z-test for proportions, and the test statistic is calculated as:

z = (p̂ - p) / √(p(1-p)/n)

where p̂ is the sample proportion, p is the hypothesized proportion (i.e. 0.22), and n is the sample size (i.e. 1189). Plugging in the values, we get:

z = (0.193 - 0.22) / √(0.22(1-0.22)/1189) = -1.96

Since we are using a significance level of 0.01, we need to compare the test statistic to the critical value of z at the 0.01 level of significance, which is -2.3263 (from the z-table). Since -1.96 is not less than -2.3263, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the series of television advertisements are less successful than the typical ad at the 0.01 level of significance.

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