Question

A Internet food delivery company advertises that it has 3 different diets that will result in weight loss if strictly followed. One diet is advertised as a moderate weight loss, a second offers a slightly more aggressive weight reduction program, and a third that is the most aggressive weight loss. The company gathers some data by taking a random sample from people using the different diets at the end of a two months trial. The data on weight loss are recorded below.

Diet 1	Diet 2	Diet 3
5	7	12
7	11	15
9	13	17
11	17	20

1. What type of data are these values?
2. Can these data be generalized? Explain.
3. Can cause and effect statements be made? Explain.
4. Conduct a test to see if the weight losses are equal with the three diets using a alpha of .05.
5. Construct 95% confidence intervals.
6. Write a brief conclusion to the CEO of this firm.

Answer 1

1. What type of data are these values?

Quantitative data as all the values are numerical.

1. Can these data be generalized? Explain.

Yes as the random sample of people is used.

1. Can cause and effect statements be made? Explain.

Yes as the type of diet will affect weight loss.

1. Conduct a test to see if the weight losses are equal with the three diets using a alpha of .05.

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Diet 1, Diet 2, Diet 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	128.0	64.00	5.43	0.028
Error	9	106.0	11.78
Total	11	234.0

Since the p-value (0.028) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that the weight losses are equal with the three diets.

1. Construct 95% confidence intervals.

Factor	N	Mean	StDev	95% CI
Diet 1	4	8.00	2.58	(4.12, 11.88)
Diet 2	4	12.00	4.16	(8.12, 15.88)
Diet 3	4	16.00	3.37	(12.12, 19.88)

Pooled StDev = 3.43188

1. Write a brief conclusion to the CEO of this firm.

The weight losses are equal with the three diets.