sample- a recent study reports that older adults who got regular physical exercise experienced fewer symptoms of depression, even when tested 2 years late.

regular excersize scores= 1,3,4,3,5,2,3,4

no regular excersize scores=5,4,6,3,5,7,6,6

a)calculate the mean and the standard deviation for each group of score.

b)based on the statistics part, does there appear to be a difference between two groups?

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my numbers look off. please help? thank you.

Group 1

mean = (1/8)* sum of your numbers, Call each Xi so (1/8)sum of Xi from i = 1 to 8
sigma^2 = (1/7)[ sum of (Xi-mean)^2] from i = 1 to 8
find sigma^2 and take the square root to find sigma
Do the same for group 2
See if the two means + or - their sigmas overlap significantly. If so, then you probably can not say much about how important exercise is to depression.

To calculate the mean and standard deviation for each group of scores, you need to follow these steps:

a) Calculate the mean for each group:
- For the regular exercise group:
Sum up all the scores and divide by the number of scores.
(1 + 3 + 4 + 3 + 5 + 2 + 3 + 4) / 8 = 25 / 8 = 3.125

- For the no regular exercise group:
Sum up all the scores and divide by the number of scores.
(5 + 4 + 6 + 3 + 5 + 7 + 6 + 6) / 8 = 42 / 8 = 5.25

b) Calculate the standard deviation for each group:
To calculate the standard deviation, you need to find the variance first. Then, take the square root of the variance.

- For the regular exercise group:
1. Calculate the variance:
a. Subtract the mean of the regular exercise group from each score in that group.
(1 - 3.125), (3 - 3.125), (4 - 3.125), (3 - 3.125), (5 - 3.125), (2 - 3.125), (3 - 3.125), (4 - 3.125)
= -2.125, -0.125, 0.875, -0.125, 1.875, -1.125, -0.125, 0.875
b. Square each of the values obtained in step (a).
(-2.125)^2, (-0.125)^2, (0.875)^2, (-0.125)^2, (1.875)^2, (-1.125)^2, (-0.125)^2, (0.875)^2
= 4.515, 0.016, 0.766, 0.016, 3.516, 1.266, 0.016, 0.016
c. Sum up all the squared values from step (b).
4.515 + 0.016 + 0.766 + 0.016 + 3.516 + 1.266 + 0.016 + 0.016 = 10.121
d. Divide the sum obtained in step (c) by the number of scores minus 1 (since it's a sample).
10.121 / (8 - 1) = 10.121 / 7 = 1.446

2. Calculate the standard deviation:
Take the square root of the variance obtained in step (e).
√(1.446) ≈ 1.202

- For the no regular exercise group:
1. Calculate the variance:
a. Subtract the mean of the no regular exercise group from each score in that group.
(5 - 5.25), (4 - 5.25), (6 - 5.25), (3 - 5.25), (5 - 5.25), (7 - 5.25), (6 - 5.25), (6 - 5.25)
= -0.25, -1.25, 0.75, -2.25, -0.25, 1.75, 0.75, 0.75
b. Square each of the values obtained in step (a).
(-0.25)^2, (-1.25)^2, (0.75)^2, (-2.25)^2, (-0.25)^2, (1.75)^2, (0.75)^2, (0.75)^2
= 0.0625, 1.5625, 0.5625, 5.0625, 0.0625, 3.0625, 0.5625, 0.5625
c. Sum up all the squared values from step (b).
0.0625 + 1.5625 + 0.5625 + 5.0625 + 0.0625 + 3.0625 + 0.5625 + 0.5625 = 11.45
d. Divide the sum obtained in step (c) by the number of scores minus 1 (since it's a sample).
11.45 / (8 - 1) = 11.45 / 7 = 1.64

2. Calculate the standard deviation:
Take the square root of the variance obtained in step (e).
√(1.64) ≈ 1.281

b) Based on the statistics part, you can compare the means and standard deviations of the two groups to determine if there appears to be a difference between the two groups. In this case, the mean for the regular exercise group is 3.125, and the mean for the no regular exercise group is 5.25. This suggests that, on average, those who engaged in regular exercise had lower scores. Additionally, the standard deviation for the regular exercise group is 1.202, while for the no regular exercise group it is 1.281. Although the standard deviations are relatively close, indicating some variability within each group, the means suggest a potential difference between the two groups. However, it is important to note that further statistical analyses, such as hypothesis testing, would be needed to confirm if the difference is statistically significant.