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 p-value obtained for this study was .0053. What do these results tell us?
a. the data provide sufficient evidence to reject H0; therefore, we conclude that there are no
differences in the mean number of pounds lost on the statistics diet and the mean
number of pounds lost on the regular low calorie diet.
b. the data provide sufficient evidence to reject H0; therefore, we conclude that the mean
number of pounds lost on the statistics diet is greater than the mean number of pounds
lost on the regular low calorie diet.
c. the data do not provide sufficient evidence to reject H0; therefore, we conclude that there
are no differences in the mean number of pounds lost on the statistics diet and the mean
number of pounds lost on the regular low calorie diet.
d. the data do not provide sufficient evidence to reject H0; therefore, we conclude that
mean number of pounds lost on the statistics diet is greater than the mean number of
pounds lost on the regular low calorie diet.
B. However, there is no data given that indicates which diet lost more pounds.
To determine what the p-value of .0053 tells us, we need to understand the concept of hypothesis testing and how p-values are interpreted.
Hypothesis testing involves evaluating two opposing hypotheses - the null hypothesis (H0) and the alternative hypothesis (HA). In this study, the null hypothesis would be that there are no differences in the mean number of pounds lost on the Statistics Diet and the mean number of pounds lost on the Regular Low Calorie Diet. The alternative hypothesis would be that there is a difference between the two means.
The p-value is a probability value that measures the strength of the evidence against the null hypothesis. It tells us how likely we would observe the data or more extreme data if the null hypothesis were true. A low p-value indicates strong evidence against the null hypothesis, while a high p-value suggests weak evidence.
In this case, the obtained p-value of .0053 is less than the typical significance level of 0.05 (often used in hypothesis testing), indicating that it is statistically significant. With a significant p-value, we have evidence to reject the null hypothesis.
Now let's evaluate the given answer choices:
a. The data provide sufficient evidence to reject H0; therefore, we conclude that there are no differences in the mean number of pounds lost on the Statistics Diet and the mean number of pounds lost on the Regular Low Calorie Diet.
This answer is incorrect because rejecting the null hypothesis means that there is evidence of a difference, not that there are no differences.
b. The data provide sufficient evidence to reject H0; therefore, we conclude that the mean number of pounds lost on the Statistics Diet is greater than the mean number of pounds lost on the Regular Low Calorie Diet.
This answer is incorrect because the given results do not provide information on which diet resulted in greater weight loss. The alternative hypothesis only states that there is a difference, not a specific direction of the difference.
c. The data do not provide sufficient evidence to reject H0; therefore, we conclude that there are no differences in the mean number of pounds lost on the Statistics Diet and the mean number of pounds lost on the Regular Low Calorie Diet.
This answer is incorrect because as mentioned earlier, the obtained p-value of .0053 is statistically significant. We have evidence to reject the null hypothesis.
d. The data do not provide sufficient evidence to reject H0; therefore, we conclude that the mean number of pounds lost on the Statistics Diet is greater than the mean number of pounds lost on the Regular Low Calorie Diet.
This is the correct answer. Since the p-value is statistically significant, we reject the null hypothesis and conclude that there is evidence that the mean number of pounds lost on the Statistics Diet is greater than the mean number of pounds lost on the Regular Low Calorie Diet.
In conclusion, the correct answer is d.