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.
Stats Diet 6 2.3 0.55
Reg.Low Cal.Diet 6 1.23 0.5

6. What is the value of the test statistic?
a. 3.53
b. -3.53
c. 11.62
d. -11.62
7. 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.

To find the test statistic, you need to calculate the t-value using the mean and standard deviation of the two groups. The formula for calculating the t-value is:

t = (mean1 - mean2) / sqrt((s1^2/n1) + (s2^2/n2))

Where:
mean1 = mean of the Statistics Diet group
mean2 = mean of the Regular Low Calorie Diet group
s1 = standard deviation of the Statistics Diet group
s2 = standard deviation of the Regular Low Calorie Diet group
n1 = number of participants in the Statistics Diet group
n2 = number of participants in the Regular Low Calorie Diet group

Plugging in the values from the table:
mean1 = 2.3
mean2 = 1.23
s1 = 0.55
s2 = 0.5
n1 = 6
n2 = 6

Substituting the values into the t-value formula:
t = (2.3 - 1.23) / sqrt((0.55^2/6) + (0.5^2/6))
t = 3.53

Therefore, the value of the test statistic is 3.53.

Now, let's move on to finding out what the p-value tells us.

The p-value obtained in this study is 0.0053. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true.

In this case, the null hypothesis (H0) would be that there is no difference in the mean number of pounds lost on the Statistics Diet and the Regular Low Calorie Diet.

Since the p-value (0.0053) is less than the commonly used significance level of 0.05, it is considered statistically significant. This means that the probability of observing a test statistic as extreme as 3.53 (or more extreme) under the assumption of no difference is very low.

Therefore, we reject the null hypothesis and 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.

In conclusion, the correct answer for question 6 is a. 3.53 and the correct answer for question 7 is 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.

To find the test statistic, we can use the formula for the two-sample t-test:

t = (mean of group 1 - mean of group 2) / sqrt((s1^2 / n1) + (s2^2 / n2))

Substituting the given values:

For the Statistics Diet group:
Mean = 2.3
Standard Deviation = 0.55
Number of participants = 6

For the Regular Low Calorie Diet group:
Mean = 1.23
Standard Deviation = 0.5
Number of participants = 6

t = (2.3 - 1.23) / sqrt((0.55^2 / 6) + (0.5^2 / 6))
= 1.07 / sqrt(0.0496 + 0.0417)
= 1.07 / sqrt(0.0913)
= 1.07 / 0.302

So, the value of the test statistic is approximately 3.53.

Therefore, the answer to question 6 is a. 3.53.

For question 7, we compare the calculated test statistic with the p-value obtained.

If the p-value is less than the significance level (commonly set at 0.05), we reject the null hypothesis (H0) and conclude that there is evidence of a difference between the two groups.

In this case, the p-value obtained is 0.0053, which is less than 0.05.

Therefore, the answer to question 7 is 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.