Question

A boutique fitness studio would like to test whether their program is affective at weight loss. They randomly select 7 female participants to adhere to their diet and exercise regimen for 12 weeks. A before and after weight in pounds was recorded for each participant. Consider all conditions to be met. Use a significance level of 0.10 and assume the population of differences is normal. Use the following to answer the questions below.

           

Participant	1	2	3	4	5	6	7
Before	165.9	138.4	149.2	121.6	177.4	122.8	191.7
After	157.3	142.5	132.4	120.6	157.7	121.2	180.1

State: Does the program promote weight-loss? In other words, is the difference between before and after greater than zero?

Plan:

a. State the null and alternative hypotheses to answer the question of interest.

      b. What type of test is appropriate to answer the question of interest and why?

c. State the significance level.

Solve:

      d. (4 points) Calculate the test statistic. State the degrees of freedom and p-value.

Participant	1	2	3	4	5	6	7
Before	165.9	138.4	149.2	121.6	177.4	122.8	191.7
After	157.3	142.5	132.4	120.6	157.7	121.2	180.1
Difference

      e. Calculate and interpret a 90% confidence interval for the average difference of weight in lbs.

Conclude:

f. Interpret the results from the hypothesis test and confidence interval in the context of the problem. Use the four part conclusion.

Answer 1

a) Null Hypothesis

ALternative Hypothesis

b) Matched pairs t test is appropriate, because for each female the weight before the program and after the program are measured.

c) Significance level

d) The computation table is given below

Participant	Before	After	D = Before-After	D^2
1	165.9	157.3	8.6	73.96
2	138.4	142.5	-4.1	16.81
3	149.2	132.4	16.8	282.24
4	121.6	120.6	1	1
5	177.4	157.7	19.7	388.09
6	122.8	121.2	1.6	2.56
7	191.7	180.1	11.6	134.56
Total			55.2	899.22

Under H0, the test statistic is

Degrees of freedom = n-1= 7-1= 6

The P-Value is 0.0276

e) 90% CI

The Confidence Interval is ( 1.426, 14.354)

f) Since p value is less than significance level. Reject H0.

Also since Confidence interval does not include zero, and have positive values for lower and upper limits, Reject H0.

Henece, the weight loss program is effective.