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(ISOM111)[2000](f)final~2106^_10357.pdf
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ISMT111 Business Statistics Final Examination 16th December 2000
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 your examination paper is missing.
3.
Key formulas and statistical tables are provided separately.
4.
You are given THREE HOURS to complete this examination. Do not start working until you are told to do so.
1. A computer company claims that its new model computer sells well, and on the average 45 units were sold per week. A consumer group suspects that the claim is inflated, and hires a statistician to test the claim. Sales data of 16 weeks were available to the statistician, and the average sales of these 16 weeks were 43.5 units per week with a sample SD of 3.0 units per week.
(a)
Set up the testing problem by identifying the hypothesis (Ho) and the
alternative (Ha).
(b)
Suppose the sales of the new computer per week has a normal distribution. Use a small-sample method to test this claim at .=2.5%.
(c)
Use a large-sample method to test this claim at .=2.5%.
[18 marks]
2. The problem is to determine the proportion (p) of women among new digital video camera buyers. A statistician wants to choose a sample size such that the resulting 95% interval estimate for p has a margin of error (error bound) no larger than 0.05.
(a)
What sample size the statistician should choose?
(b)
What sample size the statistician should choose if it can be "safely" assumed that among new digital video camera buyers, at least 72.5% are men.
[18 marks]
3. Is the mean number of miles per gallon obtained by all cars using leaded gasoline differs significantly from the mean number of miles per gallon obtained by cars using unleaded gasoline? In order to answer this question, a statistician collects gasoline mileage data for 21 cars. The data are summarized as follows:
Leaded Unleaded n1=11 n2=10 1=17.2 miles/gallon 2=18.9 miles/gallon s1=2.1 miles/gallon s2=2.0 miles/gallon
Car mileages for both leaded and unleaded gas are known to be normally
distributed.
(a)
Compute the pooled SD Sp.
(b)
Test if the average miles/gallon are different for these two groups of cars at .=5%.
(c)
It is suspected that leaded gas gives less mileage. Test it at .=5%.
[18 marks] 4. A study on the effect of bus fare (X) on the number of passengers (Y) produced the following result.
Bus fare ($) 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Passengers 800 780 740 660 640 620 600 600
per 50 km
(a)
Calculate the least squares regression line.
(b)
Interpret the least squares regression line specifically in terms of this problem.
(c)
Use the regression line in (a) to estimate the number of passengers when X=0. Do you believe in this estimate? Explain briefly using knowl