business statistics examination

8. The managing director of a social media marketing company is considering a new bonus scheme designed to increase sales volume. Currently, the mean sales value per member of the selling team is €13,300 per month. The MD is planning a research study, in which a sample of sales personnel will be allowed to sell under the new bonus scheme for a one-month period, to see whether the scheme increases sales value.

a. Formulate the null and alternative hypotheses most appropriate for this research situation.

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10. The manager of the Costa Resort Hotel stated that the mean weekend guest bill is €600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager’s claim.

a. Which form of the hypotheses should be used to test the manager’s claim? Explain.

 

H0 : m ³ 600

H1 : m < 600

 

H0 : m £ 600

H1 : m > 600

 

H0 : m = 600

H1 : m ¹ 600

 

 

12. The label on a yoghurt pot claims that the yoghurt contains an average of one gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.

a. Formulate the appropriate null and alternative hypotheses.

b. What is the Type I error in this situation? What are the consequences of making this error?

c. What is the Type II error in this situation? What are the consequences of making this error?

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