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One hundred students were placed into two groups. The two groups were the South Beach diet...

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Basic Math

One hundred students were placed into two groups. The two groupswere the South Beach diet and Keto diet. Below are the data forpounds lost after 1 month of dieting. Assume the data are normaland 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 ofyour 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 & Explanation Solved by verified expert
4.1 Ratings (537 Votes)

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.
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