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(ISMT111)f472eb - Final03.pdf
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ISMT111 Business Statistics
Final Examination

20th December 2003
Directions
1) Answer ALL SIX questions. Marks are shown in square brackets.
2) There are 6 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is
missing.
3) Key formulas and Statistical tables are provided separately.
4) Calculator may be used in this examination.
5) You are given THREE HOURS to complete this examination. Do not
begin until you are told to do so.
Question 1: [16 Marks]
The owner of a nightclub in Lan Kwai Fong has recently sampled a survey of n=100 customers who attended the club on Saturday night. He would like to determine whether or not the mean age of the customers on Saturday nights is over 30. If so, he would like to hire a new Disc Jockey to play different music to appeal to a younger crowd. Suppose that the sample mean was 30.45 years and the sample standard deviation was 5 years. Part I
(a)
State the null and alternative hypothesis. Is it appropriate to use a test based on the Normal distribution or T-distribution. Please explain your answer.

(b)
Suppose that the owner wants to be 99% sure of his decision. Based on the information will he hire a new Disc Jockey?


(c) What is the p-value associated with the test. Part II Suppose that a survey of customers was also conducted on Wednesday night, based on a sample of n=100 customers. This time the sample mean was 28 and the standard deviation was 7 years. The owner wants to know if there is a true difference in the mean age of the customers on Wednesday and Saturday nights.
(a)
What assumptions are necessary to conduct a suitable test based on the pooled variance?

(b)
Suppose that the true variability in ages on Wednesday and Saturday are the same. Using the fact that the two sample sizes are the same give the simplified general formula for the pooled variance estimator. Also give the numerical estimate based on the information in this problem.


Question 2: [16 Marks]
A battery manufacturer claims that his company produces batteries with a mean life of 130 hours. An investigator working for an independent consumer protection agency wishes to test the credibility of the manufacturers claim. She randomly selects 100 batteries produced by the process and decides that she will believe the manufacturers claim only if the sample mean is not less than 129 hours. It is known that the standard deviation of the manufacturing process is 5 hours.
(a)
What is null hypothesis, alternative hypothesis?

(b)
What is the rejection region?

(c)
What is the level of significance of the test ()?

(d)
If the investigator wishes to control the Type I error of the test to be 1%, what will be her rejection region?

(e)
If the sample mean of the 100 batteries that the investigator selected is 128 hours, what decision should she make at 1% level of significance?


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