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(isom111)[2005](f)final~750^_10362.pdf
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ISMT111 Business Statistics
Final Examination

For sections L3, 4, 5 and 6 only

20th December 2005
Directions
1) Answer ALL SIX questions. Marks are shown in square brackets.
2) There are 4 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: [12 Marks]
A weight loss company claims that on average its customers will lose more that 23 pounds in 5 weeks. To give evidence to this claim they conduct a study on 56 participants and report a sample mean of 23.5 pounds and a standard deviation of 10.2 pounds.
(a)
Write the hypothesis statement that is appropriate to check whether their claim is true or not. Conduct the test at the 5% significance level and state your conclusions. What assumption is necessary to conduct this test?

(b)
Construct a 95% confidence interval for the true mean.

(c)
Suppose that the true population standard deviation is indeed 10.2 pounds. The company now wants to make the claim that the average weight loss is more than a value A. Based on the data, find the maximum value of A (rounded down to an integer value), where the data suggests that this claim is true at the 5% significance level.



Question 2: [16 Marks]
A study was conducted to determine the difference in average gas mileage for two brands of cars, say brand1 and brand 2. Six cars of each type were tested and a 95% confidence interval for the true average difference 1-2 was given as [-6.14,16.14].
(a)
Use this information to calculate the standard error (standard deviation) of the difference between the sample means of brand 1 and brand 2. What assumption is necessary to justify this answer?

(b)
Construct a 90% confidence interval for the true average difference.

(c)
A test of hypothesis was performed to determine whether the difference between the average mileage of brand 1 and brand 2 is 10 at the 10% level of significance. The observed T-test statistic was -1. Based on this was the null hypothesis rejected?

(d)
Use parts (a)-(c) to find the value of the difference between the sample means of brand 1 and brand 2.



Question 3: [20 Marks]
An organization uses a very complicated system to determine the pension for retired employees. From the past data, a statistician found that the following simple formula seems to describe the situation quite well.
Y = 1.0 + 0.6X + 0.04X + Z
1 2,
where Y, is pension in thousand of dollars, X1, monthly salary (in thousands of dollars) right before retirement; X2, years of employment with the organization; Z is a normal random variable with mean zero and standard deviation 1. Randomly select one retired employee from those who worked for the