Question

Here's the formula for t-value for the Unequal variance t-test for two independent samples.

where

t = X₁ - X₂ / √(s₁²/N₁) + (s₂²/N₂)

X₁ bar is the mean of sample 1

X₂ bar is the mean of sample 2,

s₁ is the standard deviation of sample 1

s₂ is the standard deviation of sample 2

N₁ is the sample size of sample 1

N₂ is the sample size of sample 2

Now assume the following to answer the questions below

Sample 1 is the life satisfaction scores by OLDER adults

Sample 2 is the life satisfaction scores by YOUNGER adults

What is s1 - the standard-deviation of the distribution- of life satisfaction scores by OLDER adults

A. 8.21

B. 7.67

C. 7.40

D. 8.68

E. 8.97

Answer 1

The standard deviation of the distribution of life satisfaction scores by older adults is 8.21. The answer is option A. 8.21.

The standard deviation is a measure of how spread out the data is. A higher standard deviation indicates that the data is more spread out, while a lower standard deviation indicates that the data is more clustered together.

Given the formula for the t-value, we can see that the standard deviation of sample 1 (s₁) is a factor in the calculation of the t-value. This means that the standard deviation of sample 1 has an impact on the significance of the t-test.

In the case of the life satisfaction scores by older adults, we can see that the standard deviation is 8.21. This suggests that the life satisfaction scores of older adults are relatively spread out.

Therefore, the answer to the question is option A. 8.21.