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.
gsgs
what critical value should the company officials use to determine the rejection region?
I wanna the answer 😊
To determine if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if the population proportion of "like the ads a lot" for the company's ads is less than 0.22), we can conduct a hypothesis test using sample data.
Here's how you can perform the hypothesis test:
Step 1: State the null hypothesis (H0) and alternative hypothesis (Ha):
Null Hypothesis (H0): The population proportion of "like the ads a lot" for the company's ads is equal to or greater than 0.22.
Alternative Hypothesis (Ha): The population proportion of "like the ads a lot" for the company's ads is less than 0.22.
Step 2: Decide on the significance level (α):
Given that the significance level is 0.01.
Step 3: Collect and analyze the sample data:
Based on the study, out of 1,189 adults who viewed the ads, 230 indicated that they "like the ads a lot." This gives a sample proportion of "like the ads a lot" (p̂) of 230/1189 ≈ 0.193.
Step 4: Calculate the test statistic:
We can use the Z-test statistic to test our hypothesis. The formula for the Z-test statistic is:
Z = (p̂ - P) / sqrt(P(1-P)/n)
where P is the hypothesized population proportion, which is 0.22 in this case, and n is the sample size, which is 1189.
Calculating the test statistic:
Z = (0.193 - 0.22) / sqrt(0.22 * (1 - 0.22) / 1189)
Z ≈ -1.408
Step 5: Determine the critical value:
Since the alternative hypothesis is that the population proportion is less than 0.22, we will use a one-tailed test. At a significance level of 0.01, the critical value for a one-tailed test is approximately -2.326 (obtained from a standard normal distribution table or calculator).
Step 6: Make a decision:
Compare the test statistic (Z) with the critical value:
Z = -1.408
Critical value = -2.326
Since the test statistic (Z) is greater than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude 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. The series of television advertisements may not be less successful than the typical ad.
Note: It's important to remember that this is a hypothesis test, and the results are based on the sample data. There may be other factors to consider and potential sources of error in the study.