4.20 Taste Test A taste test is conducted between two brands of diet cola, Brand

Question

4.20 Taste Test A taste test is conducted between two brands of diet cola, Brand A and Brand B, to determine if there is evidence that more people prefer Brand A. A total of 100 people participate in the taste test.

a. Define the relevant parameter(s) and state the null and alternative hypotheses.

b. Give an example of possible sample results that would provide strong evidence that more people prefer Brand A. (Give your results as number choosing Brand A and number choosing Brand B.)

c. Give an example of possible sample results that would provide no evidence to support the claim that more people prefer Brand A.

d. Give an example of possible sample results for which the results would be inconclusive: the sample provides some evidence that Brand A is preferred but the evidence is not strong.

4.28 Red Wine and Weight Loss Resveratrol, a compound in grapes and red wine, has been shown to promote weight loss in rodents and now in a primate.10 Lemurs fed a resveratrol supplement for four weeks had decreased food intake, increased metabolic rate, and a reduction in seasonal body mass gain compared to a control group. Suppose a hypothetical study is done for a different primate species, with one group given a resveratrol supplement and the other group given a placebo. We wish to see if there is evidence that resveratrol increases the mean metabolism rate for this species. (This exercise presents hypothetical data. We will see the results from the actual study later in this chapter.)

a. Define the relevant parameter(s) and state the null and alternative hypotheses.

b. Possible sample results for species A are shown in Figure 4.7(a) with the mean indicated by a circle on the boxplots. In the sample, is the mean greater for the resveratrol group? Can we necessarily conclude that resveratrol increases the metabolism rate for this species?

Figure 4.7 Does red wine boost metabolism rates?

c. Possible sample results for species B are shown in Figure 4.7(b) and the sample sizes are the same as for species A. For which of the two species, A or B, is the evidence stronger that resveratrol increases the metabolism rate for this species? Explain your reasoning.

Explanation / Answer

Question 4.20

a. Define the relevant parameter(s) and state the null and alternative hypotheses.

Answer:

The relevant parameters for the comparing the two brands of diet cola are given as p1 and p2 where p1 is the population proportion of the people who prefer brand A and p2 is the proportion of people who prefer brand B. The null and alternative hypotheses are given as below:

Null hypothesis: H0: There is no any statistically significant difference in the population proportions of the persons who prefer brand A diet cola and who prefer brand B diet cola.

Alternative hypothesis: Ha: The proportion of the persons who prefer brand A diet cola is more than the proportion of the persons who prefer brand B diet cola.

b. Give an example of possible sample results that would provide strong evidence that more people prefer Brand A. (Give your results as number choosing Brand A and number choosing Brand B.)

Answer:

Suppose out of 100 persons, it is observed that 64 persons prefer brand A diet cola. This means about 64% persons prefer brand A. The estimate for proportion for persons prefer brand A is 0.64. So, proportion for persons preferring brand A is more than persons preferring brand B. (Expected proportion is 0.50).

c. Give an example of possible sample results that would provide no evidence to support the claim that more people prefer Brand A.

Answer:

Suppose out of 100 persons, it is observed that 44 persons prefer brand A diet cola. This means about 44% persons prefer brand A. The estimate for proportion for persons prefer brand A is 0.44. So, proportion for persons preferring brand A is not more than persons preferring brand B. (Expected proportion is 0.50).

d. Give an example of possible sample results for which the results would be inconclusive: the sample provides some evidence that Brand A is preferred but the evidence is not strong.

Answer:

Suppose out of 100 persons, it is observed that 51 persons prefer brand A diet cola. This means about 51% persons prefer brand A. The estimate for proportion for persons prefer brand A is 0.51. So, proportion for persons preferring brand A is more than persons preferring brand B, but this proportion is near to expected proportion 0.50 and that’s why there is no strong evidence that brand A is more preferred. (Expected proportion is 0.50).

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