Question

It has been suggested that night shift-workers show more variability in their output
levels than day workers. Below, you are given the results of two independent random
samples.
Night Shift Day Shift
Sample Size 10 9
Sample Mean 520 540
Sample Variance 38 20

a. state null and alternative hypotheses

b. compute test statistic

c. at the .05 level of significance, determine the critical value.

Answer 1

a. state null and alternative hypotheses

Null hypothesis: H0: The night shift-workers don’t show more variability in their output
levels than day workers.

Alternative hypothesis: Ha: The night shift-workers show more variability in their output
levels than day workers.

b. compute test statistic

Test statistic = F = S1^2/S2^2 = 38/20 = 1.90

F = 1.90

c. at the .05 level of significance, determine the critical value.

α = 0.05

df1 = n1 – 1 = 10 – 1 = 9

df2 = n2 – 1 = 9 – 1 = 8

Test is upper tailed test.

So, critical value by using F-table or excel is given as below:

Critical value = 3.3881