Question

A fitness company conducted an experiment on multiple volunteers for their 15-day “beach body” weight loss program. Their before and after weights were taken and the results are listed in the Homework 3.xlsx file on the sheet named “Problem 5”.   

a. What is the average before weight of the group?

b. What is the average after weight of the group?

Before	After
247.7	232.9
177.8	169.7
152.7	151.6
115.9	119.1
242.5	241
121.7	126.2
241.3	234.5
212.8	217.7
182.5	176.7
231.3	222.8
225.9	217.2
155.3	154.4
187.9	177.5
149.4	139.3
187.7	194.1
176.4	174.3
197.7	191.8

c. Using an appropriate confidence interval, determine if the program was effective over the 15-days in helping people lose weight.

Answer 1

Let's run the hypothesis test in Excel. We will run a paired two-sample t-test as the data is taken on the same subjects.

Ho: μd = 0

Ha: μd =/ 0

The difference between before and after is calculated in the following table:

Before	After	Difference = Before - After
247.7	232.9	14.8
177.8	169.7	8.1
152.7	151.6	1.1
115.9	119.1	-3.2
242.5	241	1.5
121.7	126.2	-4.5
241.3	234.5	6.8
212.8	217.7	-4.9
182.5	176.7	5.8
231.3	222.8	8.5
225.9	217.2	8.7
155.3	154.4	0.9
187.9	177.5	10.4
149.4	139.3	10.1
187.7	194.1	-6.4
176.4	174.3	2.1
197.7	191.8	5.9

So we need to work on the third column which is the difference. First, let's calculate the averages of first two columns using the formula of AVERAGE in excel.

a) Average of before weight = Sum/17 = 188.62

b) Average of after weight = Sum/17 = 184.75

c) d̅ = Average of the third column = 3.86

standard deviation = 6.16 (Using the formula STD.S)

Confidence interval formula is: d̅ +- t*s/√n

t-critical value at 95% confidence level and df = n - 1 = 16 is: 1.746

Now, we know all the values. Let's insert it into the formula.

Lower bound: 3.86 - 1.746*6.16/√17 = 3.86 - 2.61 = 1.25

Upper bound: 3.86 + 1.746*6.16/√17 = 3.86 + 2.61 = 6.47

Confidence interval: (1.25, 6.47)

The confidence interval does not contain 0, hence we can say that average of the differences between before and after is significantly greater than zero. Hence, the program was effective in helping people lose weight.