Question

We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20.
The test statistic is:_____
a. 1.50
b. 2.25
c. 1.56
d. .67

Answer 1

Answer:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

Now we can calculate the statistic like this:

$F=\frac{s^2_A}{s^2_B}=\frac{30^2}{20^2}=2.25$

And the best option would be:

b. 2.25

Step-by-step explanation:

Information given

$n_A = 25$ represent the sample size A

$n_B =16$ represent the sample size B

$s_A = 30$ represent the sample deviation for A

$s_B = 20$ represent the sample deviation for B

Solution to the problem

We want to test if the variation for A it's equal to the variation for B, so the system of hypothesis are:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \neq \sigma^2_2$

Now we can calculate the statistic like this:

$F=\frac{s^2_A}{s^2_B}=\frac{30^2}{20^2}=2.25$

And the best option would be:

b. 2.25