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(ISOM111)[2001](f)final~2106^_10359.pdf
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ISMT111 Business Statistics
Final Examination

18th December 2001
Directions
1) Answer ALL SIX questions. Marks are shown in square brackets.
2) There are 5 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 TWO AND A HALF HOURS to complete this examination. Do not begin until you are told to do so.
Question 1: [16 Marks]
A car manufacturer estimates that it will lose $1,000 for every car recalled due to defects. If a car is not recalled the company makes a profit of $1000 on the sale of that car.
a) The company wants to sample its current stock of cars such that a 95% interval estimate for the percentage of recalls has a margin of error no larger than 0.08. Determine the sample size for the company.
b) The company based on last years figures lost $20000 due to recalls and overall had a net profit of $1,000,000. Using this information, what is the sample size which satisfies the requirements in part a)?

Question 2: [16 Marks]
A battery company claims that on average their batteries last 60 hours
a) A sample of size 15 is obtained resulting in a sample mean of 52 hours with a sample standard deviation of 22 hours. Assume that the battery lifetimes are normally distributed with unknown mean and variance 100. Test to see whether the companies batteries really last that long with =5%.
b) Now suppose the Normal assumption still holds but exact knowledge of the variability is not assumed. Redo part a).

Question 3: [16 Marks]
In a study on the effect of coffee on performance of company workers, five workers were selected at random to take coffee and then perform a task. Seven workers were selected at random and were asked to perform the task without drinking coffee. Their performance was recorded on a scale from 0 to 100. (Higher scores indicate better performance.) The results are summarized as follows:
With coffee: sample average=60.33, sample SD=15.82
Without coffee: sample average=32.21, sample SD=12.77

It is assumed that the measures of performance for these two groups are normally distributed with means 1, 2 and variances 12,22 respectively. Past experience suggests that 12 = 22. The difference between the two means, D = 1 -2, is of interest.
a) Construct a 99% interval estimate for D.
b) Test the hypothesis that H0: D=15 vs H1: D>15 at =5%. Find the range of the
p-value.


Question 4: [17 Marks]
For a company to maintain a competitive edge in the marketplace, spending on research and development (R&D) is essential. To determine the optimum level for R&D spending and its effect on a company's market value, a simple linear regression analysis was performed. Data collected for the top 20 R&D spenders (based on 1981-1982 averages) were used to fi