Question

1. A researcher for a yogurt manufacturer would like to determine whether adult consumers showed any preference between two new yogurt products that the company recently developed, as one will be marketed as “organic” and the other without the organic designation. To start, a small sample of adults was obtained (n = 9), and on Day 1, given the organic yogurt to eat. The next day, the same 9 adults were given the non-organic yogurt to eat, with the same instructions and the same testing conditions. Participants did not know which type of yogurt (organic or nonorganic) they were eating, as both were in identical containers (that were white with green lettering). It was found that these yogurt-eaters ate, on average, 6.0 ounces more of the organic yogurt than of the non-organic product when allowed to consume as much as they wanted.

a) State an appropriate set of hypotheses for this type of repeated measures study.

b) Are your stated hypotheses directional or nondirectional?

c) Indicate an appropriate alpha level for this study.

d) The result of this t-test was t = 2.63. Using the hypotheses you provided above, what conclusion can you make about this study of yogurt eating? Please indicate the critical value from the table, as well as the degrees of freedom associated with this study and statistical test.

Answer 1

a)

Answer:

Explanation:

Since we are doing the repeated measures on the same subject, this is a paired sample design.

The null hypothesis is defined as the mean difference in the amount of organic and inorganic yogurt a person ate is zero and the alternative hypothesis test the claim the mean difference is not zero.

b)

Answer:

Nondirectional.

Explanation:

Since the researcher doesn't know which yogurt is more likely to consume by the adult, the alternative hypothesis is nondirectional.

c)

Answer:

Significance level =, alpha = 0.05

Explanation:

The most widely used value of the significance level = 0.05. (The lower level of alpha (= 0.01 or 0.001) is used when the more precise result is required for example in a diagnostic test because the human life is involved there.)

d)

Answer:

There is sufficient evidence to conclude that the organic yogurt is consumed more compared to the inorganic yogurt.

Explanation:

Test statistic

t = 2.63

P-value

The p-value is obtained from the t distribution table for t = 2.63 for the degree of freedom = n-1 = 9-1=8 for a two-tailed test

P-value = 0.0302

Conclusion

Since the p-value is less than 0.05, the null hypothesis is rejected at a 5% significance level. Hence there is sufficient evidence to conclude that the organic yogurt is consumed more compared to the inorganic yogurt.