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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

Respuesta :

Answer:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

Now we can calculate the statistic like this:

[tex]F=\frac{s^2_A}{s^2_B}=\frac{30^2}{20^2}=2.25[/tex]

And the best option would be:

b. 2.25

Step-by-step explanation:

Information given

[tex]n_A = 25 [/tex] represent the sample size A

[tex]n_B =16[/tex] represent the sample size B

[tex]s_A = 30[/tex] represent the sample deviation for A

[tex]s_B = 20[/tex] 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: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

Now we can calculate the statistic like this:

[tex]F=\frac{s^2_A}{s^2_B}=\frac{30^2}{20^2}=2.25[/tex]

And the best option would be:

b. 2.25

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