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(ISOM111)[2002](f)final~2106^_10361.pdf
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ISMT111 Business Statistics
Final Examination
18th December 2002
Directions
1) Answer ALL SEVEN 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: [14 Marks]
A researcher has collected data on the starting salaries of male and female recent graduates of an MBA program. A sample of 18 female students was taken which showed a mean salary of $43,000 per month and standard deviation of $8,000 per month. A sample of 12 male students was taken with a mean salary of $55,000 per month and a standard deviation of $11,000. Using this information answer the questions below:
(a)
The researcher wishes to test whether the average monthly salary for females is lower than that for males. Test this at a 0.05 significance level.
(b)
What are two assumptions necessary to conduct the test in part (a)?
(c)
Use the data to test whether average yearly salary (based on 12 months) of all male graduates is different from $600,000 with a significance level of 0.1.
(d)
Suppose that the true population standard deviation is $8000 per month for MBA graduates. Use the information above to construct a 95% confidence interval for the true average monthly salary of MBA graduates.
Question 2: [13 Marks]
A few years ago, Pepsi invited consumers to take the Pepsi Challenge. They wanted to know if customers preferred Coke or Pepsi in a blind taste test. Pepsi was interested in determining if gender had an effect on peoples taste preferences. They sampled 109 males where 46 said they preferred Pepsi to Coke. 52 females were sampled and 13 had a preference for Pepsi.
(a)
Use the data to determine if there is a difference between males and females preferences at a 0.1 level of significance.
(b)
Suppose that Pepsi wanted to determine whether males preferred Pepsi more than females. State the appropriate hypothesis and find the p-value of this test.
(c)
Pepsi finds the information from the sample of females useful. However they want to sample more females such that (based on the new group) the bound on the error will be less than 0.1 with 95% certainty. Find the sample size needed.
Question 3: [13 Marks]
Do the public believe that the verdict of 240 hours of social service on a pop star is adequate? A newspaper phoned 434 individuals (selected at random from the public) to ask this question, and 68.7% believed that the verdict is too lenient. An instructor of ISMT 111 asked the same question for his session of 70 students, and 46 of the students believe that the verdict is too lenient.
(a)
It is believe that the students, being young