Question

The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.5, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use = .10.

1. State the null and alternative hypotheses.

2. Calculate the value of the test statistic (to 2 decimals).

3. The p-value is

4. What is your conclusion?

Answer 1

Given : n1=n2=16 $s_1^2=2.3$    $s_2^2=5.5$    $\alpha=0.10$

1. Hypothesis :
2
   Vs $H_a:\sigma_1^2\neq \sigma_2^2$

2. The test statistic under Ho is ,

$F=\frac{s_2^2}{s_1^2}\to F_{n_2-1,n_1-1}$     $\because s_2^2>s_1^2$

$=\frac{5.5}{2.3}=2.39$

3. P value = $P(F_{d.f.}>F_{stat})=P(F_{16-1,16-1}>2.39)=0.0511$

4. Decision : Here , P value = 0.0511< $\alpha=0.10$

Therefore , reject Ho at 10% level of significance

Conclusion : Hence , there is sufficient evidence to conclude that the two production departments differ in terms of unit cost variance.