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. C
5. B
To determine the appropriate hypothesis test and the null and alternative hypotheses for this study, we need to consider the nature of the data and the research question.
The study involves comparing the effectiveness of two different diets on weight loss, specifically the Statistics Diet and the Regular Low Calorie Diet. The data collected is the number of pounds lost at the end of the first week of the diet for participants in each group.
Since we are comparing means between two different groups (Statistics Diet and Regular Low Calorie Diet), the appropriate hypothesis test would be a t-test for independent samples. This test is used to compare the means of two independent groups and assess whether they are statistically different from each other.
The null hypothesis (Ho) states that there is no difference between the means of the two groups. The alternative hypothesis (Ha) states that there is a difference between the means.
Now we can look at the given options for the null and alternative hypotheses:
a. Ho: μ1 = μ2; Ha:μ1 > μ2
This is not the correct option because it assumes a one-sided alternative hypothesis, stating that the mean of Statistics Diet is greater than the mean of Regular Low Calorie Diet. However, the alternative hypothesis could also be that the mean of Statistics Diet is less than the mean of Regular Low Calorie Diet.
b. Ho: μ1 - μ2 = 0; Ha: μ1 - μ2 ≠ 0
This is the correct option because it presents a two-sided alternative hypothesis, stating that the means of the two diets are not equal.
c. Ho: μ1 - μ2 = 0; Ha: μ1 - μ2 < 0
This option assumes a one-sided alternative hypothesis, stating that the mean of Statistics Diet is less than the mean of Regular Low Calorie Diet. However, the alternative hypothesis could also be that the mean of Statistics Diet is greater than the mean of Regular Low Calorie Diet.
d. Ho: μ1 - μ2 = 0; Ha: μ1 - μ2 > 0
This option assumes a one-sided alternative hypothesis, stating that the mean of Statistics Diet is greater than the mean of Regular Low Calorie Diet. However, the alternative hypothesis could also be that the mean of Statistics Diet is less than the mean of Regular Low Calorie Diet.
Therefore, the appropriate hypothesis test is c. t-test for independent samples, and the correct null and alternative hypotheses are b. Ho: μ1 - μ2 = 0; Ha: μ1 - μ2 ≠ 0.