Question

An eating disorders clinic would like to assess the efficacy of their 10-week mindfulness training program with clients who have Binge Eating Disorder (BED). The clinic researchers first measured the number of binges in the previous week for 16 clients through self-report. One month after the mindfulness training sessions were conducted, the clients were again asked to report the number of binges in the last week. The data are listed in the table below. The clinic researchers have set the significance level at α = .05. # of Binges per week Subject Before Training After Training

	# of Binges per week
Subject	Before Training	After Training
1	4	2
2	2	1
3	4	4
4	1	1
5	5	2
6	4	1
7	3	2
8	2	3
9	5	2
10	7	5
11	6	4
12	3	1
13	3	2
14	2	2
15	2	1
16	3	1

Part I. (25 points total) a) Identify the outcome (dependent) variable and the independent variable (that differentiates the two populations being compared). What are the “samples” in this paired-samples t test? (Or, what are the “means” in this dependent-means t test?) (1 point) b) The clinic researchers predict the number of binges per week will decrease after the mindfulness training. In other words, the researchers believe the mindfulness training will be helpful in reducing binge eating. What would be the null and alternative hypotheses in both words and symbol notations? c) Calculate the difference scores by subtracting the “before” scores from the “after” scores. (In other words, set up the columns to calculate after minus before.) Create a table below for “difference score.” d) Calculate the mean from the sample of the difference scores. e) Estimate the standard deviation of the comparison population (that represents the null hypothesis). f) Calculate the standard error (standard deviation of the sampling distribution). g) Calculate the t statistic for the sample. h) Because the hypotheses are directional, a one-tailed test can be performed. Determine the critical t value based on the degrees of freedom and the preset alpha level. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly “reject” or “fail to reject” accordingly. i) Interpret the result in 1-2 sentences (you may restate the hypothesis accepted or explain it in your own words). ( a) Calculate the raw and standardized effect size of this hypothesis test. The clinic researchers could also set up the hypothesis to see if there are any differences (increases or decreases) in binge eating behavior after mindfulness training. a) What would be the null and alternative hypotheses for this alternative analysis? Compose them in symbol notations only. b) Since a non-directional hypothesis is examined with a two-tailed test, determine the critical t values for the two-tailed test using the same alpha level and degree of freedom. c) Compare the t statistic with the critical t values. Is the calculated t statistic more extreme or less extreme than the critical t value? What is the decision of the hypothesis test now? d) Was the two-tailed test result (Part II) different from the one-tailed test result (from Part I)? Why or why not?

Answer 1

a) Independent variable is 10-week mindfulness training program.

Dependent variable is the number of binges.

b) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Null Hypothesis H0: The mean number of binges before the treatment is equal to the mean number of binge after the treatment.

Alternative hypothesis Ha: The mean number of binges after the treatment is less than the mean number of binge before the treatment.

For the score differences we have

Dˉ=−1.375 and sD​=1.204

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ < 0

This corresponds to a left-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the degrees of freedom are df=15.

Hence, it is found that the critical value for this left-tailed test is tc​=−1.753, for α=0.05 and df=15.

The rejection region for this left-tailed test is R={t:t<−1.753}.

standard error= Sd/sqrt(n)= 1.204/sqrt(16)= 1.204/4= 0.301

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that t=−4.568<tc=−1.753, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0002, and since p=0.0002<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1 (AFTER) is less than μ2(BEFORE), at the 0.05 significance level.

Note: As per the guidelines I have done the first part please re post the second part along with the data. Thank you