production departments. A sample of 16 cost reports for each of the two departments shows

cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two

production departments differ in terms of unit cost variance? Use a .10.

The situation is based on the variability in the cost of two production departments. Here, the study is carried out to investigate the claim that whether there will be significant difference in the variability of costs of two production departments. The following steps are required is to clarify the claim. Step 1: Construction of null and alternative hypotheses Null hypothesis ( H0

${H}_{0}$) : The null hypothesis states that, there is no significant difference between the population cost variances of the two production departments. This implies, the cost variance ofthe first production department (σ21)

$({\sigma}_{1}^{2})$and the cost variance ofthe second production department (σ22)

$({\sigma}_{2}^{2})$is same.i.e. H0:σ21=σ22

${H}_{0}:{\sigma}_{1}^{2}={\sigma}_{2}^{2}$Alternative hypothesis ( ): The alternative hypothesis states that,there is a significant difference between the population cost variances of the two production departments. This implies, the cost variance ofthe first production department (σ21)

$({\sigma}_{1}^{2})$and the cost variance ofthe second production department (σ22)

$({\sigma}_{2}^{2})$is not same.i.e. H1:σ21≠σ22

${H}_{1}:{\sigma}_{1}^{2}\ne {\sigma}_{2}^{2}$. Step 2: Setting up level of significance In this situation, the level of significance is 0.10. This implies, the probability of Type I error is 0.10. Step 3: Specification of sample variances At first, the sample cost variances of two production departmentsare to be specified. In this case, the number of cost reports of firstproduction departmentis denotedas n1

${n}_{1}$