University of Delhi 2010-1st Year M.Com Commerce STATISTICAL ANALYSIS UNIVERSITY - Question Paper
[This question paper contains 24 printed pages ]
Your Roll No
3TTWI
6450-
Time Wf :
Course 103 - STATISTICAL ANALYSIS (OC Admissions of 2003 and before)
3 Hours Maximum Marks 75
3 Trlfo : 75
(Write your Roll No on the top immediately on receipt of this question paper )
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Answers may be written either m English or in Hindi, but the same medium should be used throughout the paper
Note :
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Attempt all question All questions carry equal marks All the parts of a question must be answered together and in a given order
Use of simple calculator is allowed
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(a) Discuss the rules of probability
(b) An advertising executive is studying television viewing habits of married men and women during prime time-hours On the basis of past viewing records, the executive has determined that during prime time, husband are watching television 60% of the time It has also been determined that when husband is watching television 40% of the time the wife is also watching When the husband is not watching television, 30% of the time the wife is watching television Find the probability that,
(l) If the wife is watching television, the husband is also watching television (n) The wife is watching televison dunng prime time
(c) A doctor, heart specialist, has decided to prescribe three drugs to 400 heart patients as given below 100 patients were given drug A, 60 patients were given drug B, 80 patients were given drug C and the remaining patients were given all the three drugs These patients were chosen randomly so that each had 41% chance of having a heart-attack in case no drug is given Drug A reduces the probability of heart-attack by 35%, drug B reduces the probability of heart-attack by 21%, drug C reduces the probability of heart-attack by 25% and three drugs taken together work independently
( 3 ) 6450-B
Compute marginal probability of a heart-attack If a randomly selected patient has suffered from heart-attack, what is the probability the patient was given all three drugs7 (3+6+6)
Or
(a) Explain the use of decision tree in probability analysis
(b) Given the probability of three events A, B and C occurring are P(A) = 0 35, P(B) = 0 45 and P(C) = 02 Assuming that A, B or C has occurred, the probabilities of another event, X occurring are
P(X/A) = 0 8, P(X/B) = 0 65 and P(X/C) = 03 Find P(A/X), P(B/X), and P(C/X)
(c) Reliance Industries limited is determining whether it should submit bid for oil exploration contract In the past, main competitor of RIL, ONGC has submitted bids 66% of the time If ONGC does not bid for oil exploration contract, the probability that RIL will get the contract is 0 45 If ONGC does bid for oil exploration contract, the probability that RIL will still get the contract is 0 25
(i) If Reliance Industries gets the contract, what is the probability that ONGC did not bid7 (n) What is the probability that Reliance Industries will get the contract7 (3 + 6 + 6)
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2 (a) Explain Bayes' theorem
(b) Two events, A and B are statistically dependent If P(A) = 0 31, P(B) = 0 22 and P(A or B) = 0 47, find the probability that
(I) Neither A nor B will occur
(II) A will occur, given that B has occurred (in) B will occur, given that A has occurred
(iv) Both A and B will occur
(c) Mean of inner diameter (inches) of a sample of 400 tubes produced by a machine is 0 502 and the standard deviation is 0 05 The purpose for which these tubes are produced allows a maximum tolerance of 0 496 to 0 508 otherwise the tubes are considered defective What percentage of tubes produced by the machines are expected to be defective if the diameter are found to be normally distributed9 (3+6+6)
Or
(a) Discuss various approaches to the calculation of probability Under what conditions is the classical approach not appropriate to employ9
( 7 ) 6450-B
(b) The manager of finance company knows from his experience that the number of loan applications received in his office during a week is a random variable with mean, n = 66 4 and standard deviation, a = 10 9 Assuming that the distribution of the number of loan applications is approximately normal, what is the probability that the office will receive in one week,
(l) more than 75 applications,
(u) at least 75 applications,
(in) between 65 and 75 applications inclusive7
(c) During a survey of road safety it was found that 60% of accidents occur at night, 52% are alcohol related, and 37% are alcohol related and occur at night
(i) What is the probability that an accident was alcohol related given that it is occurred at night7
(n) What is the probability that an accident occurred at night, given that it was alcohol related7
(3 + 6 + 6)
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3 (a) Describe briefly the importance of normal distribution in decision-making What are its main properties7
(b) In an automotive safety test conducted by a Safety Research Centre, the average tyre pressure in a sample of 102 tyres was found to be 26 pounds per square inch and the standard deviation was 2 62 pounds per square inch
(1) What is the estimated standard deviation of the population (population consists of 40 millions tyres)9
(n) Calculate the estimated standard error of mean (in) Construct a 92 percent confidence interval for the population mean
(c) A marketing company has undertaken an advertisement campaign for a popular breakfast food
6450-B ( 10 )
that claims that it is an improved product A survey is conducted to find out the weekly demand of 11 consumers before and after the campaign Analyse the following data and tell whether the campaign was successful (use a = 0 05)
|
Before |
After |
|
14 |
23 |
|
5 |
14 |
|
18 |
13 |
|
18 |
29 |
|
30 |
33 |
|
10 |
11 |
|
8 |
12 |
|
26 |
25 |
|
13 |
21 |
|
29 |
26 |
|
24 |
34 |
Or
(a) Explain the procedure for testing of hypothesis
(b) Institute of Chartered Accountants was considering a proposal to require companies to report the potential effects of employees' stock options (ESOP) on its earning per share (EPS) A random sample of 49 software companies revealed that the new proposal would reduce EPS by an average of 13 95 percent, with a standard deviation of 19 1 percent Another sample of 39 drug manufacturing companies
( 11 ) 6450-B
showed that the proposal would reduce EPS by 12 9 percent on an average, with a standard deviation of 8 95 percentage On the basis of these samples, is it reasonable to conclude (at a = 0.10%) that the proposal of Institute of Chartered Accountants will cause a greater reduction m EPS of software companies than for drug manufacturing companies
(c) Ten computer printer dealers in a town were asked to submit their prices for two similar colour inkjet printers Prices are given below
|
Dealers |
Apson price |
HP price |
|
1 |
250 |
270 |
|
2 |
319 |
325 |
|
3 |
285 |
269 |
|
4 |
260 |
275 |
|
5 |
305 |
289 |
|
6 |
295 |
285 |
|
7 |
289 |
295 |
|
8 |
309 |
325 |
|
9 |
275 |
300 |
|
10 |
299 |
301 |
Using i-test, at a = 0 05, is it reasonable to assert that, on an average, the Apson printer is less expensive than HP printer9 (3 + 6 + 6)
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( 13 ) 6450-B
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4 (a) Explain the role of probable value m hypothesis testing
(b) Using the %2 test with 0 05 level of significance
analyse the following table that gives the number of users of a new shampoo What conclusion can you draw about the pattern of demand in different regions7
|
Region | ||||
|
NW |
NE |
SW |
SE | |
|
Do not buy |
60 |
45 |
55 |
50 |
|
Buy |
40 |
55 |
45 |
50 |
(c) The supervisor of security at a large department store would like to know whether the store apprehends relatively more shoplifters during the Christmas holidays than in the weeks before or after the holidays He collected data on the number of shoplifters apprehended in the store during the
( 15 ) 6450-B
months of November, December and January over the past six years which are given below
November
December
January
|
43 |
37 |
59 |
55 |
38 |
48 |
|
54 |
41 |
48 |
35 |
50 |
49 |
|
36 |
28 |
34 |
41 |
30 |
32 |
At the 0 05 level of significance, is the average number of apprehended shoplifters the same dunng three months9 (3 + 6 + 6)
Or
(a) Explain the properties of a good estimator
(b) A production manager feels that the output rate of experienced employees is certainly greater than that of new employees, but he does not expect the variability in output rates to differ for the two groups In previous studies, it has been shown that the average unit output per hour for new employees at this particular type of work is 20 units per hour with a variance of 56 units squared For a group of 20 employees with 5 year experience, the average output for this same type of work is 30 units per hour, with a sample variance of 28 units squared Does the variability in output differ at the two experience levels9 Test the hypotheses at the 0 05 significance level9
(c) Data on the martial status for men and women ages 20 to 29 were obtained as part of the national survey The results from a sample of 2,450 men and 2,500 women are as follows
|
Martial Status | ||||||||||||
|
Using a = 0 01, test for independence between martial status and gender, what is your conclusion9
(3+6+6)
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What is Z-distribution9 Explain its main properties The first proof of 200 pages of a book containing 560 pages revealed the following distribution of the number of printing errors
(a)
(b)
No of errors in a page No of pages
0 112
1 63
2 20
3 3
4 1
5 1 Total 200
( 19 ) 6450-B
Fit a Poisson distribution to these data and test the goodness of fit (a = 0 05)
(c) Realfacts, a real research firm, provides monthly mean apartment rental cost for a metropolitan city Assume the population standard deviation is $220 and the desired margin of error is $50 (i) What is the recommended sample size for a 90% confidence interval estimate of the population mean rental cost9 (u) What is the recommended sample size for a 95% confidence interval9 (in) What is the recommended sample size for a 99% confidence interval9 (3+6+6)
Or
(a) Critically evaluate the utility of non-parametnc tests
(b) The Federal Reserve is performing a preliminary study to determine the relationship between certain economic indicators and annual percentage change in the gross national product (GNP) Two such indicators being examined are the amount of federal government deficit (m billions dollars) and the Dow Jones industrial average (the mean value over the year) Data for six years are given below
| |||||||||||||||||||||
|
(1) Calculate the least square equation that best |
describes the data (u) What percentage change in GDP would be expected m a year m which the federal deficit was $240 and the mean Dew Jones value was 3,000?
(c) A flight operations analyst has been assigned the task of monitoring flights at the company's airport 250 takeoffs are scheduled every day from the airport The analyst is concerned about the fraction of flights with late departures, and four weeks ago he instituted procedures designed to reduce that fraction Use the data for last thirty weekdays to construct a p-chart to see whether his new procedures have been successful
|
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6450-B | |
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Sixth Week | |
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14 |
18 |
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17 |
|
W |
20 |
13 |
16 |
|
TH |
18 |
9 |
18 |
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F |
18 |
10 |
17 |
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| Earning: Approval pending. |
