Question

question 41
a sample with a variance of s² = 36 has a standard deviation equal to s = 6.
true
false
question 42
the sum of the squared deviation scores is ss = 20 for a sample of n = 6 scores. what is the variance for this sample?
s² = 4
s² = 5
s² = 80
s² = 100
question 43
for a population of scores, the sum of the deviation scores is equal to 0.
true
false

Explanation:

Question 41

Step1: Recall standard - deviation formula

The formula for the standard deviation $s$ of a sample is $s = \sqrt{s^{2}}$, where $s^{2}$ is the variance.

Step2: Calculate standard deviation

Given $s^{2}=36$, then $s=\sqrt{36}=6$.

Question 42

Step1: Recall sample - variance formula

The formula for the sample variance $s^{2}=\frac{SS}{n - 1}$, where $SS$ is the sum of squared deviations and $n$ is the sample size.

Step2: Substitute values

Given $SS = 20$ and $n = 6$, then $s^{2}=\frac{20}{6 - 1}=\frac{20}{5}=4$.

Question 43

Step1: Recall deviation - score property

The sum of deviation scores $\sum(X-\mu)=0$ for a population, where $X$ are the individual scores and $\mu$ is the population mean. This is because the positive and negative deviations from the mean cancel each other out.

Answer:

Question 41: True
Question 42: $s^{2}=4$
Question 43: True