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 determine the test statistic, we can use the formula for comparing two independent sample means. The formula is:

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

Given the following values:
mean1 = 2.3
mean2 = 1.23
s1 = 0.55
s2 = 0.5
n1 = 6
n2 = 6

Plugging the values into the formula, we get:

t = (2.3 - 1.23) / sqrt((0.55^2 / 6) + (0.5^2 / 6))

t = 1.07 / sqrt(0.0347 + 0.0278)

t = 1.07 / sqrt(0.0625)

t = 1.07 / 0.25

t = 4.28

Therefore, the value of the test statistic is 4.28.

The p-value obtained for this study was 0.0053. To interpret the results:

Since the p-value (0.0053) is less than the typical significance level of 0.05, we can conclude that the data provide sufficient evidence to reject H0 (null hypothesis). Therefore, the correct option 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 determine the value of the test statistic, we need to perform a t-test for independent samples.

First, let's calculate the pooled standard deviation using the formula:

Sp = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))

where n1 and n2 are the sample sizes, and s1 and s2 are the standard deviations of the two groups.

In this case, the sample sizes are both 6, and the standard deviations are 0.55 and 0.5 for the Statistics Diet and Regular Low Calorie Diet groups, respectively.

Sp = sqrt(((6-1)*0.55^2 + (6-1)*0.5^2) / (6 + 6 - 2)) = sqrt((0.8925 + 0.875) / 10) = sqrt(0.17625) = 0.42

Next, we calculate the test statistic, which is given by:

t = (x1 - x2) / (Sp * sqrt(1/n1 + 1/n2))

where x1 and x2 are the means of the two groups, and n1 and n2 are the sample sizes.

In this case, the means are 2.3 and 1.23 for the Statistics Diet and Regular Low Calorie Diet groups, respectively.

t = (2.3 - 1.23) / (0.42 * sqrt(1/6 + 1/6)) = 3.53

Therefore, the value of the test statistic is 3.53.

For question 7, the p-value obtained for this study is given as 0.0053.

The p-value represents the probability of observing a test statistic as extreme as the one calculated (or even more extreme) if the null hypothesis (H0) were true.

In this case, our null hypothesis states that there are no differences 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 significance level typically chosen (e.g., 0.05), we can conclude that the data provide sufficient evidence to reject H0.

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.