A researcher was interested in assessing the effectiveness of the Statistics Diet as
compared to a regular low calorie diet on weight loss. In the study, obese participants were
randomly assigned to one of two groups: (1) the Statistics Diet, which required participants
to calculate the mean number of calories in each food that they ate at every meal or (2) the
Regular Low Calorie Diet, which had participants consume only 1000 calories a day. The
dependent/response measure collected was the number of pounds lost at the end of the
first week of the diet. The following table contains the results of the study.
Number of Participants Mean Standard Dev
Statistics Diet 6 2.3 0.55
Reg.Low Calorie Diet 6 1.23 0.5
4. What is the appropriate hypothesis test?
a. z-test
b. t-test for matched pairs
c. t-test for independent samples
d. chi square test for independence
5. What are the null and alternative hypotheses?
a. Ho:μ1=μ2; Ha:μ1>μ2
b. Ho:μ1−μ2=0; Ha:μ1−μ2≠0
c. Ho:μ1−μ2=0; Ha:μ1−μ2<0
d. Ho:μ1−μ2=0; Ha:μ1−μ2>0
4. The appropriate hypothesis test for this study is c. t-test for independent samples. This is because we have two independent groups (Statistics Diet and Regular Low Calorie Diet) and we want to compare the means of these two groups.
5. The null and alternative hypotheses are:
Null Hypothesis (Ho): μ1 - μ2 = 0
Alternative Hypothesis (Ha): μ1 - μ2 < 0
In other words, the null hypothesis states that there is no difference in the mean weight loss between the Statistics Diet group and the Regular Low Calorie Diet group, while the alternative hypothesis states that the mean weight loss in the Statistics Diet group is less than the mean weight loss in the Regular Low Calorie Diet group.
To determine the appropriate hypothesis test, we need to consider the nature of the study design and the type of data collected.
In this study, the obese participants were randomly assigned to two groups, the Statistics Diet group and the Regular Low Calorie Diet group. Each group had their own diet plan, and the number of pounds lost at the end of the first week was measured as the dependent/response variable.
Since the two groups were assigned different diets and the participants are independent of each other, we are comparing the means of two independent samples. Therefore, the appropriate hypothesis test for this scenario is the t-test for independent samples.
Now, let's move on to the null and alternative hypotheses. The null hypothesis (Ho) states that there is no difference in the mean weight loss between the two diets, while the alternative hypothesis (Ha) states that there is a difference in the mean weight loss between the two diets.
We can express these hypotheses as follows:
Ho: μ1 - μ2 = 0 (Mean weight loss in the Statistics Diet group is equal to the mean weight loss in the Regular Low Calorie Diet group)
Ha: μ1 - μ2 ≠ 0 (Mean weight loss in the Statistics Diet group is not equal to the mean weight loss in the Regular Low Calorie Diet group)
Therefore, the answer to question 5 is option b. Ho:μ1−μ2=0; Ha:μ1−μ2≠0.