Question

One hundred students were placed into two groups. The two groups were the South Beach diet and Keto diet. Below are the data for pounds lost after 1 month of dieting. Assume the data are normal and that the sample size is 100 (but, use the values you have). Tell me if there is a difference between the two diets. Show all of your work.

SB	Keto
2.5	3.5
3.2	3.7
3.0	4.0
5	4.1
2.3	4.0
2.7	2.5
1.0	2.3

Answer 1

We know,

Mean = Total Sum / No. of Samples

Variance = Sum of Squares of Deviation from Mean / No. of Samples

Standard Deviation = Square Root of Variance

Hence, the table follows :

Sl. No.	SB Group			Keto Group
	Data	Deviation from Mean	Square Deviation from Mean	Data	Deviation from Mean	Square Deviation from Mean
1	2.50	-0.31	0.10	3.50	0.06	0.00
2	3.20	0.39	0.15	3.70	0.26	0.07
3	3.00	0.19	0.03	4.00	0.56	0.31
4	5.00	2.19	4.78	4.10	0.66	0.43
5	2.30	-0.51	0.26	4.00	0.56	0.31
6	2.70	-0.11	0.01	2.50	-0.94	0.89
7	1.00	-1.81	3.29	2.30	-1.14	1.31
Sum	19.70		8.63	24.10		3.32
No. of Sample	7		7	7		7
Mean	2.81			3.44
Variance			1.23			0.47
Standard Deviation			1.11			0.69

Hence,

Mean and Standard Deviation of both diets are clearly different. So, we can surely conclude that there is difference between two diets.