Suppose a clinic provides a program to help their clients lose weight and asks a

Question

Suppose a clinic provides a program to help their clients lose weight and asks a consumer agency to investigate the effectiveness of the program. The agency randomly samples 15 people in the program, weighing each person before the program begins and again three months later. The data (weight in lbs.) for each person is provided in the SPSS ‘weight-spring2016’.(Bottom) Answer the following questions

a. What kind of statistical test is appropriate here? Why?

b. What are the null and alternative hypotheses? (Make these two-tailed.)

c. Report the mean and sample standard deviation for each condition.

d. What is tobt? How many degrees of freedom are there? What is tcrit ( = 0.012tail)?

e. Report the p value of tobt from SPSS.

f.What is your conclusion about H0, using = .012tail? What is the basis for your decision? In addition to stating whether the null should be rejected or not, say what that conclusion MEANS in the context of this particular situation.

g.Calculate Cohen’s d for these data (see handout!) and interpret the result as a small, medium, or large effect size.

h. (5 pts) Based on the decision about the null hypothesis, the effect size estimate, and general considerations about statistical power, what should the agency conclude about the effectiveness of the weight loss program? Justify your answer in a few sentences.

i. Calculate the Pearson correlation coefficient for weight in the two conditions using SPSS. What is the null hypothesis? What is the alternative hypothesis? What is robt? How many degrees of freedom are there? What is rcrit ( = 0.052tail)? Report the p value (significance) of robt from SPSS. What can the researcher conclude about the correlation?   

SPSS ‘weight-spring2016’

Before After

1.   210.00   200.00

2.   205.00   195.00

3.   193.00   191.00

4.   182.00   174.00

5.   259.00   236.00

6.   239.00   236.00

7.   164.00   159.00

8.   197.00   196.00

9.   222.00   201.00

10.   211.00   196.00

11.   187.00   191.00

12.   175.00   164.00

13.   186.00   187.00

14.   243.00   233.00

15.   246.00   237.00

Explanation / Answer

a) PAIRED SAMPLE T- TEST SUITABLE FOR THIS DATA SET SINCE SAME TEST VARIABLE THAT IS WEIGHT SPRING IS COLLECTED BEFORE AND AFTER PROGRAM .

b) Null hypothis H0: There is no significance difference between means of wieght of clients before and after program.

Ha: There is statistically significance difference between means of weight if clients before and after program

c) mean and standard deviation in each report is given below ( using SPSS)

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

before

207.7333

15

28.73640

7.41971

after

199.7333

15

25.48239

6.57953

d)

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

before - after

8.00000

7.89213

2.03774

3.62948

12.37052

3.926

14

.002

  
t value obtained = 3.926

The number of degrees of freedom = n-1 = 15-1= 14

Critical value of t at 14 degrees offreedom and 95% confidence interval= 2.9714

e) p value associated with this test is = .002

f) Since p value associated with t test is less that .01 ( p=.002) we can reject null hypothesis and there by concluding there is significant difference between means of clients before and after program of clinical provider

h) Based on the result we got from paired t test research can confidently say to clinical provider that clients are loosing thier weights after the treatement started. The treatmet has been successfull

i) Pearson correlation coefficient for paied sample is given below

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

before & after

15

.965

.000

Null hypothesis: H0; There is no statistical relation between weight loss before and after the program ( R=0)

Ha: There is correlation between weight loss before and after the program (R=/0)

Correlation coffecient obtained r= .965

There are 15 degrees of freedom

P value associated with correlation test is p= 0.000

R critical value with 15 df is r = 0.482 with 5% level of significance

Since p value associated with test is lesthan 0.05 , we reject null hypothesis and there conclude that there is strong ositive correlation exist between weights of two paired sample

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

before

207.7333

15

28.73640

7.41971

after

199.7333

15

25.48239

6.57953

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