Question

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 (i.e.. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22) at a 0.01 level of significance. Referring to the above, the null hypothesis will be rejected if the test statistic is:

Answer 1

Explanation:

We would set up the hypothesis test.

For the null hypothesis,

P = 0.22

For the alternative hypothesis,

P < 0.22

This is a left tailed test

Considering the population proportion, probability of success, p = 0.22

q = probability of failure = 1 - p

q = 1 - 0.22 = 0.78

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 230

n = number of samples = 1189

p = 230/1189 = 0.19

We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.19 - 0.22)/√(0.22 × 0.78)/1189 = - 2.5

Recall, population proportion, p = 0.22

We want the area to the left of 0.22 since the alternative hypothesis is lesser than 0.22. Therefore, from the normal distribution table, the probability of getting a proportion < 0.22 is 0.00621

So p value = 0.00621

Since alpha, 0.01 > than the p value, 0.00621, then we would reject the null hypothesis.

Referring to the above, the null hypothesis will be rejected if the test statistic is - 2.5