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.
#of Participants Mean Standard Dev.
Statistics Diet 6 2.3 0.55
Reg.Low Cal.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 the two groups (Statistics Diet and Regular Low Calorie Diet) are independent of each other and the researcher wants to compare the means of each group.
5. The null and alternative hypotheses for this study are:
Null Hypothesis (Ho): The mean difference in weight loss between the Statistics Diet group and the Regular Low Calorie Diet group is zero (μ1 - μ2 = 0).
Alternative Hypothesis (Ha): The mean difference in weight loss between the Statistics Diet group and the Regular Low Calorie Diet group is less than zero (μ1 - μ2 < 0).
To determine the appropriate hypothesis test, we need to consider the study design and the nature of the data.
In this study, the researcher is comparing the effectiveness of two different types of diets on weight loss. The participants were randomly assigned to one of the two groups (Statistics Diet or Regular Low Calorie Diet). The dependent measure collected is the number of pounds lost at the end of the first week.
Since the study involves comparing the means of two different groups, the appropriate hypothesis test is the independent samples t-test.
Therefore, the answer to question 4 is: c. t-test for independent samples.
Now let's move on to question 5 to determine the null and alternative hypotheses.
The null hypothesis (Ho) states that there is no difference between the mean weight loss of participants on the Statistics Diet (μ1) and the mean weight loss of participants on the Regular Low Calorie Diet (μ2). The alternative hypothesis (Ha) states that there is a difference between the means.
In this case, since the alternative hypothesis does not specify a direction (whether one mean is greater than or less than the other), the appropriate alternative hypothesis is a two-tailed alternative.
Therefore, the answer to question 5 is: b. Ho:μ1−μ2=0; Ha:μ1−μ2≠0.