A researcher wished to test the effect of the addition of extra calcium to yogurt on the "tastiness" of yogurt. Two different yogurts, one with extra calcium and one without the added calcium, were created from the same batch of yogurt. A group of 84 adult volunteers participated in the survey, and 42 were assigned to the extra calcium group and 42 were assigned to the plain yogurt group. The first group tasted the yogurt containing extra calcium and the second group tasted the yogurt without the added calcium. Both groups rated the taste on a 10-point scale with 1 being "very unpleasant" and 10 being "very pleasant."

Identify the design of this study.

A) paired t-test of a mean
B) two-sample t-test of means
C) one sample t-test of a mean
D) one sample z-test of a proportion

B?

The correct answer is B) two-sample t-test of means.

In this study, the researcher created two different yogurts - one with extra calcium and one without - from the same batch of yogurt. Two groups of participants were assigned to each type of yogurt: one group tasted the yogurt with extra calcium, and the other group tasted the yogurt without the added calcium. Both groups then rated the taste on a 10-point scale.

The design of this study involves comparing the means (average ratings) of two different groups (yogurts with and without extra calcium). This type of comparison is typically done using a two-sample t-test of means.

A paired t-test of a mean (option A) would involve comparing the means of the same group before and after some intervention or treatment. In this study, two separate groups were formed and compared, so a paired t-test is not applicable.

A one-sample t-test of a mean (option C) would be used if you had a single group and wanted to compare its mean against a known or hypothesized value. However, in this study, we have two separate groups with different yogurts, so a one-sample t-test is not appropriate.

A one-sample z-test of a proportion (option D) would be used if we were comparing proportions or percentages between two groups. However, in this study, we are comparing the means (ratings) on a 10-point scale, not proportions.

Therefore, the appropriate design for this study is a two-sample t-test of means (option B).