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Carpetland salespersons average $7,000 per week in sales. Steve Contois, the firm's vice president, proposes a...

Carpetland salespersons average $7,000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.

(a)

Develop the appropriate null and alternative hypotheses.

H0: μ = 7,000

Ha: μ ≠ 7,000

H0: μ ≤ 7,000

Ha: μ > 7,000

    

H0: μ > 7,000

Ha: μ ≤ 7,000

H0: μ ≥ 7,000

Ha: μ < 7,000

H0: μ < 7,000

Ha: μ ≥ 7,000

(b)

What is the type I error in this situation? What are the consequences of making this error?

It would be concluding μ ≤ 7,000 when the plan does increase sales. This mistake could result in not implementing a plan that would increase sales.It would be concluding μ < 7,000 when the plan does increase sales. This mistake could result in not implementing a plan that would increase sales.    It would be concluding μ ≥ 7,000 when the plan does not increase sales. This mistake could result in implementing the plan when it would not help.It would be concluding μ > 7,000 when the plan does not increase sales. This mistake could result in implementing the plan when it would not help.

(c)

What is the type II error in this situation? What are the consequences of making this error?

It would be concluding μ ≤ 7,000 when the plan does increase sales. This mistake could result in not implementing a plan that would increase sales.It would be concluding μ < 7,000 when the plan does increase sales. This mistake could result in not implementing a plan that would increase sales.    It would be concluding μ ≥ 7,000 when the plan does not increase sales. This mistake could result in implementing the plan when it would not help.It would be concluding μ > 7,000 when the plan does not increase sales. This mistake could result in implementing the plan when it would not help.

math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution:-

(a)

Where H0 is the null hypothesis.

Where Ha is the alternate hypothesis.

Option B is correct.

(b)

It would be concluding μ > 7000 when the plan does not increase sales.

This mistake could result in implementing the plan when it would not help

Option D is correct.

(c)

It would be concluding μ ≤ 7,000 when the plan does increase sales.

This mistake could result in not implementing a plan that would increase sales

Option A is correct.

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