Question

Consider a study that compares the Atkins diet to a conventional diet. A study at the University of Pennsylvania selected a sample of 63 subjects from the local population of obese adults. Researchers randomly assigned 33 to the Atkins diet and 30 subjects to a conventional diet. Test whether there is a significant difference in the mean weight loss (measured in pounds) across the two different diet programs.

Using software:

1. Generate summary statistics (central tendency and variability measures) for the two samples and briefly summarize what they say.

b.         Conduct a test of significance for the difference between the mean sales across the two different locations in the store. Be sure to show the output from the software and interpret the results.

c. Construct a 95% confidence interval for the difference parameter in mean sales and make an interpretation.

d. Finally, are there any other factors, besides where the product is placed, that could possibly influence sales (identify at least 2)? Include a brief explanation of each.

Atkins	Conventional
27	26
31	26
34	29
31	24
28	25
32	22
33	27
27	24
34	25
25	28
31	30
26	27
28	25
30	23
26	20
26	22
31	29
34	28
27	21
28	25
33	22
26	24
26	22
30	25
26	29
34	24
25	26
32	21
29	22
33	21
27
29
25

Answer 1

(a)->

Summary statistics

Descriptive Statistics: Atkins, Conventional

Statistics

Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Atkins	33	0	27.364	0.614	3.525	20.000	25.000	27.000	30.500	34.000
Conventional	30	0	26.767	0.712	3.901	21.000	24.000	26.000	29.000	34.000

(b)->

Two-Sample T-Test and CI: Atkins, Conventional

Method

μ₁: mean of Atkins

µ₂: mean of Conventional

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Atkins	33	27.36	3.53	0.61
Conventional	30	26.77	3.90	0.71

Estimation for Difference

Difference	95% CI for Difference
0.597	(-1.285, 2.479)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
0.63	58	0.528

Here P- value is very large value i.e. 0.528. so we don't have sufficient evidence to reject the null hypothesis.

Hence there is no significance difference between the mean sales across the two different locations in the store.

(c)->

95% confidence interval for the difference parameter in mean sales is (-1.285, 2.479).

i.e. the difference between the population mean difference between the two sales across the two different locations is lies between -1.285 and 2.479 with 95% confidence.

(d)->

The possible factors of weight loss other than diet are:

(1) Some samples may loss their weight due to their poor health condition.

(2) Average weight of one location may differ from the other location. and higher the weight, easier to loss the weight. so this may be other factors which affect the weight loss.

(3) Quality of life of different places may be different.