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Bingel [31]
3 years ago
6

The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean s

ales volume is 24 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.a. Which form of the null and alternative hypotheses most appropriate for this situation. H0: is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24) Ha: is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24)b. Comment on the conclusion when H0 cannot be rejected. (No evidence that the new plan increases sales./ The research hypothesis ? > 24 is supported; the new plan increases sales.)c. Comment on the conclusion when H0 can be rejected. (No evidence that the new plan increases sales./ The research hypothesis ? > 24 is supported; the new plan increases sales.)
Mathematics
1 answer:
Tcecarenko [31]3 years ago
6 0

Answer:

The most appropriate null hypothesis for this situation is

H_0: The mean sales volume is equal to 24.

the most appropriate alternative hypothesis for this situation is

H_a: The mean sales volume is greater than 24.

Step-by-step explanation:

<em>The null hypothesis H_0 is the fact that is established and consider as true fact. </em>

Since the established mean sales volume is 24 automobiles per month this should be considered as the null hypothesis.

So, the most appropriate null hypothesis for this situation is

H_0: The mean sales volume is equal to 24

<em>The alternative hypothesis is a fact that intends to reject or refute the null by collecting data that could contradict it. </em>

In this case, since the manager wants to conduct a research study to see whether the new bonus plan increases sales volume, he wants to see if the data collected after the new bonus plan can show that the new average is greater than the established one.  

So, the most appropriate alternative hypothesis for this situation is

H_a: The mean sales volume is greater than 24.

To try and prove that H_a shows enough evidence as to assure the new plan actually increases sales volume, he must fix a significance level \alpha, for example 0.1 or 0.05, which gives the probability that H_a is not wrong in case that it rejects H_0.

This confidence level defines an \alpha-score z_\alpha which is a point such that the area under the normal curve N(0;1) to the right of z_\alpha is less than \alpha.

<em>In this case we considered the right side because you want to see the new average is greater than the established one. </em>

<em> If the z-score obtained through the sample is greater than z_\alpha then you can say the new bonus actually increases sales. </em>

<em>If the z-score obtained through the sample is less than or equals to z_\alpha then you do not have enough evidence showing that the new bonus actually increases sales.</em>

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