problemsheet_4

# problemsheet_4 - Q1 Independent random samples from normal...

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Q1 Independent random samples from normal distributions with equal variance of the amount of insider trading during mergers by employees of (1) investment banking firms and (2) brokerage houses gave the results listed in the accompanying table. Find the 95% confidence interval estimate for the difference between means μ 1 μ 2 . (1) Investment Banking Firm 10 5 5 5 8 8 8 (2) Brokerage House 6 0 5 2 2 3 3 Q2 State Senator Hanna Rowe has ordered an investigation of the large number of boating accidents that have occurred in the state in recent summers. Acting upon her instructions, her aide, Geoff Spencer, has randomly selected 9 summer months within the last few years and has compiled data on the number of boating accidents that occurred during each of these months. The mean number of boating accidents to occur in these 9 months was 31, and the standard deviation in this sample was nine boating accidents per month. Geoff was told to construct a 90% confidence interval for the true mean number of boating accidents per month, but he was in such an accident himself recently, so you will have to do this for him. Q3 The local chamber of commerce wants to estimate μ , the average amount of money spent per week for groceries by families of size 4, assuming this amount of money follows approximately a normal distribution. A random sample of 9 families of size 4 is taken, of which the mean and standard deviation of the amount of money spent per week for groceries are \$81.50 and \$10.36 respectively. Calculate a 99% confidence interval for μ . Q4 An employee of American Manufacturing, Inc., wishes to know if normally distributed managerial salaries are higher for those who have worked their way from nonmanagerial positions in the company or for those who were hired from outside the company. The employee randomly selects 10 of each type of manager. The mean annual income for those hired from outside he computes to be \$31,750, and the mean figure for the insiders is \$27,000. The corresponding standard deviation are \$6350 and \$4050. Find a 90% confidence interval for the difference in annual income of the two groups. Should this interval lead the employee to conclude that there is a real difference?

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Q5 A bank’s loan department found that 57 home loans processed during April had a mean value of \$78,100 and a standard deviation of \$6300. An analysis of the loans in May, a total of 66, showed a mean value of \$82,700 with a standard deviation of \$7100. Suppose these home loans represent random samples of the values of home loan applications approved in the bank’s service area. Find a 98% confidence interval for the difference in the mean level of approved home loan applications from April to May. Q6
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## This note was uploaded on 09/18/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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problemsheet_4 - Q1 Independent random samples from normal...

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