Question

The manager of an automobile company is considering implementing a new compensation plan designed to increase sales volume. Currently, the mean sales volume

is 17 automobiles per month. The manager wants to conduct a research study to see whether the new plan actually increases sales volume.

To collect data on the plan, a sample of sales personnel are given the new compensation program and then their sales volume is recorded after a month.

a.Write the null and alternative hypotheses that are most appropriate for this situation.

Interpret the alternative hypothesis in words.

b.In words, describe what type I and type II errors would be for this situation.

Answer 1

In this problem we are provided with the current mean sales volume which is 17 automobiles per month. We want to test whether the new plan actually increases sales volumes.

a> Let ₁ denotes the sales per month in the current compensation plan and ₂ the sales per month in the new compensation plan. We are to test H_o : ₁ =   ₂ ag H_A :    ₂ >  ₁.  

The alternative hypothesis indicates that the new compensation plan yields more sales per month than the current compensation plan.

b> Type I Error = Prob of rejecting H_o when it is true. i.e., the chance that the sample indicates that the new plan increases sales volume although the two plans produce the same amount of sales.

Type II Error = Prob of accepting H₀ when it is false i.e., the chance that the sample indicates that the two plans produce the same amount of sales although the new one gives more sales than the current one.