A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. In the accompanying table are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Suppose that the two-tail p-value was really 0.0734. State the proper conclusion. Males: n = 109 Females: n = 52 P_M = 0.422018 P_F = 0.25 P_M - P_F = 0.172018 Z = 2.11825 A. At ? = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. B. At ? = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. C. At ? = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. D. At ? = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
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- Null hypothesis (\(H_0\)): The proportion of males preferring Pepsi equals the proportion of females preferring Pepsi (\(P_M = P_F\)). - Alternative hypothesis (\(H_a\)): The proportion of males preferring Pepsi differs from the proportion of females Show more…
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A few years ago, Pepsi invited consumers to take the Pepsi Challenge. Consumers were asked to decide which of 2 sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's test preferences. One of the factors studied was a gender of the consumer. Below are the results of analyses comparing the test preferences of men and women with the proportions depicting preference for Pepsi. Males n = 109, pm = 0.422 Females n = 52, pf = 0.25 Pm - pf = .172 Z = 2.118 Suppose a 90% confidence interval estimate between the difference in proportion of males and females who prefer Pepsi is (0.05, 0.30). We use this confidence interval to determine if a difference exists in the taste preference of men and women. Our conclusion should be that: The proportion of men who prefer Pepsi is not the same as the proportion of women who prefer Pepsi The proportion of men who prefer Pepsi is the same as the proportion of women who prefer Pepsi The number of men who prefer Pepsi is not the same as the number of women who prefer Pepsi The number of men who prefer Pepsi is the same as the number of women who prefer Pepsi
Madhur L.
Two of the biggest soft drink rivals, Pepsi and Coke, are very concerned about their market shares. The pie chart that follows claims that PepsiCo's share of the beverage market is 24%. Assume that this proportion will be close to the probability that a person selected at random indicates a preference for a Pepsi product when choosing a soft drink. A group of n = 500 consumers is selected and the number preferring a Pepsi product is recorded. Use the normal curve to approximate the following binomial probabilities. (Round your answers to four decimal places.) (a) Exactly 120 consumers prefer a Pepsi product. (b) Between 110 and 120 consumers (inclusive) prefer a Pepsi product. (c) Fewer than 120 consumers prefer a Pepsi product. (d) Would it be unusual to find that 245 of the 500 consumers preferred a Pepsi product? Yes No If this were to occur, what conclusions would you draw? Pepsi's market share estimate is accurate. Pepsi's market share is lower than claimed. Pepsi's market share is higher than claimed.
Shaiju T.
Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9 - 1 along with "Table" answers based on Table $A$ - 3 with df equal to the smaller of $\boldsymbol{n}_{I}-\boldsymbol{I}$ and $\boldsymbol{n}_{2}-\boldsymbol{I} .$ ) Regular Coke and Diet Coke Data Set 26 "Cola Weights and Volumes" in Appendix B includes weights (b) of the contents of cans of Diet Coke $(n=36, \bar{x}=0.78479 \text { lb, } s=0.00439$ lb) and of the contents of cans of regular Coke $(n=36, \bar{x}=0.81682 \mathrm{lb}, s=0.00751 \mathrm{lb})$ a. Use a 0.05 significance level to test the claim that the contents of cans of Diet Coke have weights with a mean that is less than the mean for regular Coke. b. Construct the confidence interval appropriate for the hypothesis test in part (a). c. Can you explain why cans of Diet Coke would weigh less than cans of regular Coke?
Inferences from Two Samples
Two Means: Independent Samples
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