(a) the test statistic (b) the critical z score
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16b7b9ee-61a6-4d22-bbcb-acc05d2fde78%2F5a7d0409-f499-4dcd-a9d4-badfb65d6f85%2Foie0j4l_processed.jpeg&w=3840&q=75)
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
Favorable no. of outcomes
Sample size
Assume the level of significance
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