QA- PAPER -I Marks: 70 Time: 2.50 Hours

Q-1 Explain the following:

(a) What is sampling distribution? Define standard error of mean in sampling. Also write statement of central limit theorem. And write advantages of sampling.

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(b) Write a brief note on Testing of hypothesis and discuss Type-I and Type -II errors with examples. [07]

Q-2 Answer the following:(a) The administrator of SAL hospital surveyed the number of days 200

randomly chosen patients in the hospital following an operation. Calculate Mean, SD and mode for the data given below. If the distribution is roughly bell shaped, how many stays can we expect between 0 to 17 days? And what percentage of stays would you expect if the distribution is non symmetric for the same range?

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(b) A telephone survey conducted by the maritz marketing research company found that 43% of Americans expect to save money next year than they saved last year. Forty five percent of those surveyed plan to reduce debt next year. Of those who expect to save more money next year, 81% plan to reduce debt next year. An American is selected randomly.a. What is the probability that this person to expects to save more

money next year and plans to reduce debt next year?b. What is the probability that this person expects to save more

money next year or plans to reduce debt next year?c. What is the probability that this person neither expects to save

more money next year nor plans to reduce debt next year?d. What is the probability that this person expects to save more

money next year and does not plan to reduce debt next year?

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OR

Hospital stay in days Observed Frequencies1-3 184-6 907-9 44

10-12 2113-15 916-18 919-21 422-24 5

(b) The manager of a small postal substation is trying to quantify the variation in the weekly demand for mailing tubes. She has seceded to assume that the demand is normally distributed. She knows that on an average 100 tubes are purchased weekly and that 90% of the time, weekly demand is below 115.

a) What is the standard deviation of this distribution?b) The manager wants to stock enough mailing tubes each week so that

the probability of running out of tubes is no higher than 0.05. What is the lowest stock level?

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Q-3 Answer the following:(a) To see whether silicon chip sales are independent of where the U.S. economy is in the business cycle, data have been collected on the weekly sales of zippy chippy, a

silicon valley firm, and on whether the U.S. economy was rising to a cycle peak, at a cycle peak, falling to a cycle trough, or at a cycle trough. The results are:

WEEKLY SALESEconomy High Medium Low Total

At Peak 20 7 3 30At trough 30 40 30 100Rising 20 8 2 30Falling 30 5 5 40

Total 100 60 40 200

a) Calculate a table of observed and expected frequencies for this problem.

b) State the null and alternative hypotheses.c) Calculate chi-square statistics.d) At the 0.10 significance level, what is your conclusion?

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(b) The average cost per square foot for office rental space in the central business district of Philadelphia is 23.58, according to Cushman. A large real estate company wants to confirm this figure. The firm conducts the telephonic survey of 95 offices in the central business district of Philadelphia and asks the office managers how much they pay in rent per square foot. Suppose the sample average is 22.83 per square foot, with a SD of 5.11.

a) Conduct a hypothesis test using Alpha = 0.05 to determine whether the cost per square foot reported by Cushman should be rejected?

b) If in the decision in part (a) is fail to reject and if the actual cost per square foot is 22.30, what is the probability of committing type II error?

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OR(a) An important proposal must be voted on, and a politician wants to find the

proportion of people who are in favor of the proposal. Find the sample size needed to estimate the true proportion to within +.05 at the 95% confidence level. Assume you have no strong feelings about what the proportion is. How would your sample size change if you believe about 75% of the people favor the proposal? How would it change if only about 25% of the people favor the proposal?

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(b) Data of Sales generated through four different training methods are as follows: test the effectiveness of all four methods at 5% level of significance and draw the conclusion.

Method 1 Method 2 Method 3 Method 445 48 43 4149 51 45 4446 45 47 4750 41 49 5042 44 51 53

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Q-4 Answer the following:(a) A survey of CPAs across the US found that the average net income for sole

proprietor CPAs is $74, 914. Because this survey is now more than seven years old, an accounting researcher wants to test this figure by taking a random sample of 112 sole proprietor accountants in the US with average net income $78, 695 to determine whether the net income figure changed. Assume the population standard deviation of net incomes for sole proprietor CPAs is $14, 530 and 0.05 level of significance?

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(b) For the following find the best fitting line. Also find co-efficient of determination, 95% CI for expenditure when income is 20,000.

Income Expenditure25K 1800029K 2200035K 2450042K 2800022K 1650018K 1400012K 9600

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OR(a) ABC, a multinational manufacturer, uses a batch process to produce widgets.

Each batch of widgets takes 8 hours to produce and has material and labor costs of $8476. Because of variations in machine efficiency and raw material purity, the number of widgets per batch is random. All widgets made can be sold for $ 2.50 each, and widget production is profitable so long as the batches sell for more than $12,500 on average. ABC sampled 16 batches and found 5040 widgets per batch on average, with a standard deviation of 41.3 widgets. At level of significance 0.025, can ABC conclude that its widget operation is profitable?

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(b) Write a detailed note on Multicolinearity and steps to overcome the same. [07]

Q-5 Answer the following:(a) For the following data calculate Laspeyers and Pasches index Numbers by

taking 1990 as a base period.

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(b) Some oil speculators are interested in drilling an oil well. The rights to the land have been secured and they must decide whether to drill. The states of nature are that oil is present or that no oil is present. Their two decision alternatives are drill or don’t drill. If they strike oil, the well will pay $1 million. If they have a dry hole, they will lose $100,000. If they don’t drill, their payoffs are $0 when oil is present and $0 when it is not. The probability that oil is present is .11. Use this information to construct a decision table and compute an expected monetary value for this problem.

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OR(a) For Alpha = 0.4 find MSE using Exponential Smoothing and 4-

Moving averages methods for the following data and compare both the answers.

Year Housing Units

1984 17501985 17421986 18051987 16201988 14881989 13761990 11931991 10141992 12001993 12881994 14571995 13541996 14771997 14741998 16171999 1666

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(b) Write a short note on Different type of data measurement and its characteristic. [07]

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Selling Price1990 1991 199223 26 2431 35 3227 29 2621 28 2718 25 27

Number Sold

1990 1991 1992

4 2 3

6 8 5

9 5 1

2 4 7