(a) the test statistic (b) the critical z score

MATLAB: An Introduction with Applications
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**Title: Hypothesis Testing in Marketing Campaigns**

According to a recent marketing campaign, 90 drinkers of either Diet Coke or Diet Pepsi participated in a blind taste test to determine their preferred beverage. In a Pepsi television commercial, an announcer claimed that "in recent blind taste tests, more than half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that out of these 90 participants, 50 preferred Diet Pepsi. We aim to test the hypothesis, using a significance level \( \alpha = 0.05 \), that more than half of all participants will select Diet Pepsi in a blind taste test.

To conduct this test, we need to determine:

(a) **The Test Statistic:** [This will be calculated based on the sample data.]

(b) **The Critical \( z \) Score:** [This will be determined from the standard normal distribution table corresponding to \( \alpha = 0.05 \).]

The final conclusion will determine if there is sufficient statistical evidence to support the claim that more than half of the participants preferred Diet Pepsi over Diet Coke.
Transcribed Image Text:**Title: Hypothesis Testing in Marketing Campaigns** According to a recent marketing campaign, 90 drinkers of either Diet Coke or Diet Pepsi participated in a blind taste test to determine their preferred beverage. In a Pepsi television commercial, an announcer claimed that "in recent blind taste tests, more than half of the surveyed preferred Diet Pepsi over Diet Coke." Suppose that out of these 90 participants, 50 preferred Diet Pepsi. We aim to test the hypothesis, using a significance level \( \alpha = 0.05 \), that more than half of all participants will select Diet Pepsi in a blind taste test. To conduct this test, we need to determine: (a) **The Test Statistic:** [This will be calculated based on the sample data.] (b) **The Critical \( z \) Score:** [This will be determined from the standard normal distribution table corresponding to \( \alpha = 0.05 \).] The final conclusion will determine if there is sufficient statistical evidence to support the claim that more than half of the participants preferred Diet Pepsi over Diet Coke.
Expert Solution
Step 1: Determine the given data in the question

Let p be the population proportion.

Given that,

Population proportion left parenthesis p right parenthesis equals 1 half equals 0.5

Favorable no. of outcomes left parenthesis x right parenthesis equals 50

Sample size left parenthesis n right parenthesis equals 90

Assume the level of significance left parenthesis alpha right parenthesis equals 0.05


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