Question

Supervisors at Amalgated Slurries, Inc, are interested in determining if the variances of the output of day and night shifts are the same. The following samples are drawn:

Sample Statistic Day Night

Sample Size 21 26

Standard Deviation 11 16

Test the equality of the variances of the populations, using a= 0.05.

Answer 1

H₀:

H₁:

The test statistic F = s1^2/s2^2

                               = (11)^2/(16)^2

                               = 0.473

At = 0.05, the critical values are F(0.025, 20, 25) = 0.4174

                                                       F(0.975, 20, 25) = 2.3005

Since the test statistic value lies between the critical values (0.4174 < 0.473 < 2.3005), so we should not reject the null hypothesis.

So at alpha = 0.05, we can conclude that the two population variances are equal.