Question

A researcher is interested in the effects of a new weight loss supplement. Participants in this double-blind study are randomly assigned to either a group that receives the new supplement or a group that receives a placebo. Participants are weighed before starting the program. After 6 weeks of taking either the new supplement or the placebo, participants return to the lab to be weighed.

Provide the appropriate null and alternative hypotheses.
Determine which type of analysis would be appropriate to answer this research question. Be specific and support your answer using the textbook or other course materials.
Name the independent and dependent variables used in the analysis. What are the levels of the independent variable?
Indicate the levels of measurement for each variable.
Describe the Type I error for this study.
Describe the Type II error for this study.

Answer 1

A researcher in interested in testing the effects of a new weight loss supplement.

Basically, the researcher wants to understand if the weight loss supplements works in reality, or it does not. Thus, the researcher forms 2 groups. One group of people actually take the weight loss supplement, and the other group only takes a fake medicine (that is a placebo). This fake medicine is provided becuase many a time, the change is psychological. Thus, by giving both the groups some medicine, the researcher effectively leads the two groups to believe that they have been observed under the same conditions.

Group 1= group which takes the supplement

Group 2= group which takes the placebo

Thus, the null hypothesis is that the weight loss supplement has no effect and that the means of the two groups are the same.

Thus,

H₀ : 1 2

The alternate hypothesis is that the two groups have unequal means.

Thus,

H_a : 1 2

To answer this research question, the perfect study would be a two- sample t test. T tests are used to meaasure the population means, and check if there is a relation between them. Here, we have two groups, and we must check if these two groups do in fact have the same means (null hypothesis) and are not different, or if they have different means (alternate hypothesis) and are different.

A two- sample t test works perfectly to this end, and can be used in our case.

A type 1 error is when the null hypothesis is true, but you reject it. In our study, we would commit a type 1 error if group1 and group2 do in reality have equal means, but we reject this claim, and hypothesize that the means of group1 and group2 are different.

A type 2 error is when the null hypothesis is not true, but we fail to reject it (or accept it). In our sstudy, we would commit a type 2 error if group1 and group2 do in reality have different or unequal means, but we fail to reject the null hypothesis (or accept it), and hypothesize that the means of group1 and group2 are the same.