Question

We are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following Store A Store B nA=21 nB=16 SA=28.284 SB=20 The test statistic is _______________.

Answer 1

Answer:

$F=\frac{s^2_A}{s^2_B}=\frac{28.284^2}{20^2}=1.99996$

Step-by-step explanation:

Data given and notation  

$n_A = 21$ represent the sampe size for A

$n_B =16$ represent the sample size for B

$s_A = 28.284$ represent the sample deviation for A

$s_B = 20$ represent the sample deviation for B

$\alpha$ represent the significance level provided

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

$F=\frac{s^2_1}{s^2_2}$

Solution to the problem  

System of hypothesis

We want to test if we have the same variation, so the system of hypothesis are:

H0: $\sigma^2_A = \sigma^2_B$

H1: $\sigma^2_A \neq \sigma^2_B$

Calculate the statistic

Now we can calculate the statistic like this:

$F=\frac{s^2_A}{s^2_B}=\frac{28.284^2}{20^2}=1.99996$