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(ISOM111)[2006](f)final~ac_lfyab^_10364.pdf
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ISMT111 Business Statistics
Final Examination
For sections L3, L4, only
15th December 2006

Directions
1) Answer ALL SIX questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper including the cover page. 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: [18 Marks]
Data on the monthly service fee in dollars when a customers account falls below the minimum required $5000 balance for a sample of 26 banks yields a sample mean of 71.5 and a sample standard deviation of 30.55.
(a)
Please find a 95% confidence interval for the population mean monthly service fee.

(b)
Can we say that with probability 0.95 the interval obtained in (a) will include the population mean? If not, then what is the correct interpretation? Explain briefly.

(c)
Data on 10 more banks were added so that the sample size increased to 36 and we obtained a 95% confidence interval [59.55, 80.45]. What is the mean of the sample of 36?

(d)
Continue from (c). What is the standard error for the sample mean?

(e)
Assume that the estimated population standard deviation in (d) equals the true population s.d. What is the minimum sample size required so that the length of the 95% interval is less than 16?

(f)
Continue from (c). If there are four banks in the sample of 36 do not charge monthly service fee when the balance fall below $5000. Please find a 95% confidence interval for the proportion of banks that do not charge monthly service fee.



Question 2: [ 16 Marks]
One way to measure the economic outlook is the percentage of employers hiring new employees. A survey conducted by the government last year showed that 66 of the 150 employers recruiting new employees. A similar survey this year reveals that 90 of 180 employers hiring new employees.
(a)
An economist would like to test the hypothesis that the economic outlook this year is better than last year using the data on hiring new employees. State the null and alternative hypotheses.

(b)
Carry out the test and draw your conclusion using 5% significance level.

(c)
What is the p-value of the test in (b)?

(d)
Suppose the economist later found out a very accurate estimate 0.44 is available for the proportion p1 of employers hiring new employees last year. Therefore he assumes p1 =0.44 and


decide to use {p. > 0.5} as the rejection region for the null hypothesis H : p = 0.44 . What
2 02
is the probability of type I error for this rejection region?

Question 3: [16 Marks]
A statistics professor would like to demonstrate the concept of sampling distributions to a group of students. He used the computer to generate 1000 samples of s