What is your conclusion based on the following data?


A survey was conducted to study the effects of weight loss from a low fat diet. Two random samples of 100 people each were selected. One group was put on the low fat diet and the other group on the regular diet. The weight gain of the individual was measured. We want to determine whether there is any difference between the population mean weight losses from two diets. α = 0.05.

LOWFAT 8 sample mean 1 9.31
LOWFAT 10 sample mean 2 7.4
LOWFAT 10 t 3.095390373
LOWFAT 12 P-value 0.00127807
LOWFAT 9
LOWFAT 3
LOWFAT 11
LOWFAT 7
LOWFAT 9
LOWFAT 2
LOWFAT 21
LOWFAT 8
LOWFAT 9
LOWFAT 2
LOWFAT 2
LOWFAT 20
LOWFAT 14
LOWFAT 11
LOWFAT 15
LOWFAT 6
LOWFAT 13
LOWFAT 8
LOWFAT 10
LOWFAT 12
LOWFAT 1
LOWFAT 7
LOWFAT 10
LOWFAT 13
LOWFAT 14
LOWFAT 4
LOWFAT 8
LOWFAT 12
LOWFAT 8
LOWFAT 10
LOWFAT 11
LOWFAT 19
LOWFAT 0
LOWFAT 9
LOWFAT 10
LOWFAT 4
LOWFAT 11
LOWFAT 7
LOWFAT 14
LOWFAT 12
LOWFAT 11
LOWFAT 12
LOWFAT 4
LOWFAT 12
LOWFAT 9
LOWFAT 2
LOWFAT 4
LOWFAT 3
LOWFAT 3
LOWFAT 5
LOWFAT 9
LOWFAT 9
LOWFAT 4
LOWFAT 3
LOWFAT 5
LOWFAT 12
LOWFAT 3
LOWFAT 12
LOWFAT 7
LOWFAT 13
LOWFAT 11
LOWFAT 11
LOWFAT 13
LOWFAT 12
LOWFAT 18
LOWFAT 9
LOWFAT 6
LOWFAT 14
LOWFAT 14
LOWFAT 18
LOWFAT 10
LOWFAT 11
LOWFAT 7
LOWFAT 9
LOWFAT 7
LOWFAT 2
LOWFAT 16
LOWFAT 16
LOWFAT 11
LOWFAT 11
LOWFAT 3
LOWFAT 15
LOWFAT 9
LOWFAT 5
LOWFAT 2
LOWFAT 6
LOWFAT 5
LOWFAT 11
LOWFAT 14
LOWFAT 11
LOWFAT 6
LOWFAT 9
LOWFAT 4
LOWFAT 17
LOWFAT 20
LOWFAT 10
REGULAR 6
REGULAR 6
REGULAR 5
REGULAR 5
REGULAR 2
REGULAR 6
REGULAR 10
REGULAR 3
REGULAR 9
REGULAR 11
REGULAR 14
REGULAR 4
REGULAR 10
REGULAR 13
REGULAR 3
REGULAR 8
REGULAR 8
REGULAR 13
REGULAR 9
REGULAR 3
REGULAR 4
REGULAR 12
REGULAR 6
REGULAR 11
REGULAR 12
REGULAR 9
REGULAR 8
REGULAR 5
REGULAR 8
REGULAR 7
REGULAR 6
REGULAR 2
REGULAR 6
REGULAR 8
REGULAR 5
REGULAR 7
REGULAR 16
REGULAR 18
REGULAR 6
REGULAR 8
REGULAR 13
REGULAR 1
REGULAR 9
REGULAR 8
REGULAR 12
REGULAR 10
REGULAR 6
REGULAR 1
REGULAR 0
REGULAR 13
REGULAR 11
REGULAR 2
REGULAR 8
REGULAR 16
REGULAR 14
REGULAR 4
REGULAR 6
REGULAR 5
REGULAR 12
REGULAR 9
REGULAR 11
REGULAR 6
REGULAR 3
REGULAR 9
REGULAR 9
REGULAR 14
REGULAR 2
REGULAR 10
REGULAR 4
REGULAR 13
REGULAR 8
REGULAR 1
REGULAR 1
REGULAR 4
REGULAR 9
REGULAR 4
REGULAR 1
REGULAR 1
REGULAR 5
REGULAR 6
REGULAR 14
REGULAR 0
REGULAR 7
REGULAR 12
REGULAR 9
REGULAR 5
REGULAR 9
REGULAR 12
REGULAR 7
REGULAR 9
REGULAR 8
REGULAR 9
REGULAR 8
REGULAR 10
REGULAR 5
REGULAR 8
REGULAR 0
REGULAR 3
REGULAR 4
REGULAR 8

To determine whether there is any difference between the population mean weight losses from two diets, we can perform a two-sample t-test. This involves comparing the means of the two samples and calculating a test statistic (t-value) and a p-value.

Given the following data:

Low Fat Diet (Sample 1):
8, 10, 10, 12, 9, 3, 11, 7, 9, 2, 21, 8, 9, 2, 2, 20, 14, 11, 15, 6, 13, 8, 10, 12, 1, 7, 10, 13, 14, 4, 8, 12, 8, 10, 11, 19, 0, 9, 10, 4, 11, 7, 14, 12, 11, 12, 4, 12, 9, 2, 4, 3, 3, 5, 9, 9, 4, 3, 5, 12, 3, 12, 7, 13, 11, 11, 13, 12, 18, 9, 6, 14, 14, 18, 10, 11, 7, 9, 7, 2, 16, 16, 11, 11, 3, 15, 9, 5, 2, 6, 5, 11, 14, 11, 6, 9, 4, 17, 20, 10

Regular Diet (Sample 2):
6, 6, 5, 5, 2, 6, 10, 3, 9, 11, 14, 4, 10, 13, 3, 8, 8, 13, 9, 3, 4, 12, 6, 11, 12, 9, 8, 5, 8, 7, 6, 2, 6, 8, 5, 7, 16, 18, 6, 8, 13, 1, 9, 8, 12, 10, 6, 1, 0, 13, 11, 2, 8, 16, 14, 4, 6, 5, 12, 9, 11, 6, 3, 9, 9, 14, 2, 10, 4, 13, 8, 1, 1, 4, 9, 4, 1, 1, 5, 6, 14, 0, 7, 12, 9, 5, 9, 12, 7, 9, 8, 9, 8, 10, 5, 8, 0, 3, 4, 8

We can calculate the sample means for each group:

Sample mean 1 (Low Fat Diet): 9.31
Sample mean 2 (Regular Diet): 7.4

Next, we calculate the test statistic (t-value) and the p-value:

t-value: 3.095390373
P-value: 0.00127807

Finally, based on the given significance level α = 0.05, if the p-value is less than α (0.00127807 < 0.05), we reject the null hypothesis and conclude that there is a significant difference between the population mean weight losses from the two diets.

Therefore, based on the data provided, we can conclude that there is a difference between the population mean weight losses from the low fat diet and the regular diet.