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THIS PAPER IS NOT TO BE REMOVED FROM THE EXAMINATION HALLS

University of London BBA0040

BSc Examination 2011 for External Students

Business Administration

Business Statistics

DATE

DO NOT TURN OVER UNTIL TOLD TO BEGIN

Time allowed: TWO hours Answer ALL Questions

All questions carry equal marks

Electronic calculators may be used. These should be of a hand-held non-

programmable (where relevant) type and the name and model should be stated

CLEARLY on the front of your answer book.

Appropriate statistical tables are attached, you may not necessarily need to use them all.

PLEASE TURN OVER

© University of London 2011

UL11/

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1. If two events are collectively exhaustive, what is the probability that

one or the other occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

2. If two events are collectively exhaustive, what is the probability that

both occur at the same time?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

3. If two events are mutually exclusive, what is the probability that one

or the other occurs?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

4. If two events are independent, what is the probability that they

both occur?

a) 0.

b) 0.50.

c) 1.00.

d) Cannot be determined from the information given.

5. The probability that house sales will increase in the next 6 months is

estimated to be 0.25. The probability that the interest rates on

housing loans will go up in the same period is estimated to be 0.74.

The probability that house sales or interest rates will go up during the

next 6 months is estimated to be 0.89. The probability that both

house sales and interest rates will increase during the next 6 months

is:

a) 0.10

b) 0.185

c) 0.705

d) 0.90

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6. The probability that house sales will increase in the next 6 months is

estimated to be 0.25. The probability that the interest rates on

housing loans will go up in the same period is estimated to be 0.74.

The probability that house sales or interest rates will go up during the

next 6 months is estimated to be 0.89. The probability that neither

house sales nor interest rates will increase during the next 6 months

is:

a) 0.11

b) 0.195

c) 0.89

d) 0.90

7. The probability that house sales will increase in the next 6 months is

estimated to be 0.25. The probability that the interest rates on

housing loans will go up in the same period is estimated to be 0.74.

The probability that house sales or interest rates will go up during the

next 6 months is estimated to be 0.89. The events of increase in

house sales and increase in interest rates in the next 6 months are

a) statistically independent.

b) mutually exclusive.

c) collectively exhaustive.

d) None of the above.

8. The probability that house sales will increase in the next 6 months is

estimated to be 0.25. The probability that the interest rates on

housing loans will go up in the same period is estimated to be 0.74.

The probability that house sales or interest rates will go up during the

next 6 months is estimated to be 0.89. The events of increase in

house sales and no increase in house sales in the next 6 months are

a) statistically independent.

b) mutually exclusive.

c) collectively exhaustive.

d) (b) and (c)

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TABLE 1

An alcohol awareness task force at a Big-Ten university sampled 200

students after the midterm to ask them whether they went bar hopping

the weekend before the midterm or spent the weekend studying, and

whether they did well or poorly on the midterm. The following result

was obtained.

Did Well on Midterm Did Poorly on Midterm

Studying for Exam 80 20

Went Bar Hopping 30 70

9. Referring to Table 1, what is the probability that a randomly

selected student who went bar hopping will do well on the

midterm?

a. 30/100 or 30%

b. 30/110 or 27.27%

c. 30/200 or 15%

d. (100/200)*(110/200) or 27.50%

10. Referring to Table 1, what is the probability that a randomly

selected student did well on the midterm or went bar hopping the

weekend before the midterm?

a) 30/200 or 15%

b) (80+30)/200 or 55%

c) (30+70)/200 or 50%

d) (80+30+70)/200 or 90%

11. Referring to Table 1, what is the probability that a randomly

selected student did well on the midterm and also went bar

hopping the weekend before the midterm?

a) 30/200 or 15%

b) (80+30)/200 or 55%

c) (30+70)/200 or 50%

d) (80+30+70)/200 or 90%

12. Referring to Table 1, the events "Did Well on Midterm" and "Studying

for Exam" are

a) statistically dependent.

b) mutually exclusive.

c) collective exhaustive.

d) None of the above.

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13. Referring to Table 1, the events "Did Well on Midterm" and "Studying

for Exam" are

a) not statistically dependent.

b) not mutually exclusive.

c) collective exhaustive.

d) None of the above.

14. Referring to Table 1, the events "Did Well on Midterm" and "Did

Poorly on Midterm" are

a) statistically dependent.

b) mutually exclusive.

c) collective exhaustive.

d) All of the above.

A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). P(X)=[n!/X!(n-X)!]pX(1-p)n-X (you can use the statistical tables provided to answer the following questions, no need for calculations)

15. Given the above information, the probability that all 3 businesses

succeed is ________.

16. Given the above information, the probability that all 3 businesses fail is ________.

17. Given the above information, the probability that at least 1 business

succeeds is ________. 18. Suppose a 95% confidence interval for μ has been constructed. If it

is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would ________.(Assume that the sample statistics gathered would not change very much for the new sample.)

(a) be narrower than the current interval width

(b) be larger than the current interval width

(c) be the same as the current interval width

(d) be unknown until actual sample sizes and reliability levels were

determined

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The number of power outages at a nuclear power plant has a Poisson distribution P(X)=(e-λ λX)/X! (where lambda (λ) is the mean and the variance and e=2.71 ) with a mean of 6 outages per year. (You can use the statistical tables provided to answer the following questions, no need for calculations) 19. The probability that there will be exactly 3 power outages in a year

is ____________. 20. The number of power outages at a nuclear power plant has a

Poisson distribution with a mean of 6 outages per year. The probability that there will be at least 3 power outages in a year is ____________.

21. The number of power outages at a nuclear power plant has a

Poisson distribution with a mean of 6 outages per year. The probability that there will be at least 1 power outage in a year is ____________.

22. The number of power outages at a nuclear power plant has a

Poisson distribution with a mean of 6 outages per year. The probability that there will be no more than 1 power outage in a year is ____________.

23. The number of power outages at a nuclear power plant has a

Poisson distribution with a mean of 6 outages per year. The variance of the number of power outages is ____________.

24. How many Kleenex tissues should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: average= 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

a) H0: μ=60 and H1: μ≠60

b) H0: μ≤60 and H1: μ>60 X

c) H0: μ>60 and H1: μ<60

d) H0: μ≥60 and H1: μ<60

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The personnel director of a large corporation wishes to study absenteeism

among clerical workers at the corporation’s central office during the year.

A random sample of 25 clerical workers reveals the following: absenteeism

X (average)= 9.7 days, S=4 days, 12 clerical workers were absent more

than 10 days.

25. Construct a 95% confidence interval estimate of the mean number

of absences of clerical workers last year. tc=2.06

a) (9.37, 10.03)

b) (8.05, 11.35)

c) (7.64, 11.76)

d) (1.46, 17.94)

26. Construct a 95 % confidence interval estimate of the population

proportion of clerical workers absent more than 10 days last year.

Zc=1.96, p+Zc{p(1- p)/n}1/2 and p-Zc{p(1-p)/n}1/2

a) (9.68, 9.72)

b) ( (9.50, 9.90)

c) (0.46, 0.50)

d) (0.28, 0.68)

27. What would be the critical Z value in the above question if you had

to construct a 97% confidence interval?

a) 1.88

b) 1.96

c) 2.17

d) 2.33

28. What would be the critical Z value in the above question if you had

to construct a 99% confidence interval?

a) 1.88

b) 1.96

c) 2.17

d) 2.32

29. If we wish to determine whether there is evidence that the

proportion of successes is the same in group 1 as in group 2, the

appropriate test to use is

a) The F test.

b) The chi squared test.

c) Both of the above.

d) None of the above.

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30. Suppose a 95% confidence interval for turns out to be (1,000,

2,100). Give a definition of what it means to be “95% confident” in

an inference.

a) In repeated sampling, the population parameter would fall in

the given interval 95% of the time.

b) In repeated sampling, 95% of the intervals constructed would

contain the population mean.

c) 95% of the observations in the entire population fall in the

given interval.

d) 95% of the observations in the sample fall in the given interval.

31. Suppose a 95% confidence interval for turns out to be (1,000,

2,100). To make more useful inferences from the data, it is desired to

reduce the width of the confidence interval. Which of the following

will result in a reduced interval width?

a) Increase the sample size.

b) Decrease the confidence level.

c) Both increase the sample size and decrease the confidence

level.

d) Both increase the confidence level and decrease the sample

size.

32. Suppose a 95% confidence interval for has been constructed. If it

is decided to take a larger sample and to decrease the confidence

level of the interval, then the resulting interval width would

. (Assume that the sample statistics gathered would not

change very much for the new sample.)

a) be larger than the current interval width

b) be narrower than the current interval width

c) be the same as the current interval width

d) be unknown until actual sample sizes and reliability levels were

determined

33. In the construction of confidence intervals, if all other quantities are

unchanged, an increase in the sample size will lead to a

interval.

a) narrower

b) wider

c) less significant

d) biased

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34. True or False: In forming a 90% confidence interval for a population

mean from a sample size of 22, the number of degrees of freedom

from the t distribution equals 22.

35. True or False: Other things being equal, as the confidence level for

a confidence interval increases, the width of the interval increases.

36. True or False: Other things being equal, the confidence interval for

the mean will be wider for 95% confidence than for 90%

confidence.

37. True or False: The t distribution is used to develop a confidence

interval estimate of the population mean when the population

standard deviation is unknown.

38. If, as a result of a hypothesis test, we reject the null hypothesis when it is

false, then we have committed

a) a Type II error.

b) a Type I error.

c) no error.

d) an acceptance error.

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TABLE 2

An investment specialist claims that if one holds a portfolio that moves

in opposite direction to the market index like the S&P 500, then it is

possible to reduce the variability of the portfolio's return. In other

words, one can create a portfolio with positive returns but less

exposure to risk.

A sample of 26 years of S&P 500 index and a portfolio consisting of

stocks of private prisons, which are believed to be negatively related

to the S&P 500 index, is collected. A regression analysis was performed

by regressing the returns of the prison stocks portfolio (Y) on the returns

of S&P 500 index (X) to prove that the prison stocks portfolio is

negatively related to the S&P 500 index at a 5% level of significance.

The results are given in the following EXCEL output.

Coefficients Standard

Error

T Stat P-value

Intercept 4.866004258 0.35743609 13.61363441 8.7932E-13

S&P -0.502513506 0.071597152 -7.01862425 2.94942E-07

39. Referring to Table 2, to test whether the prison stocks portfolio is

negatively related to the S&P 500 index, the appropriate null and

alternative hypotheses are, respectively,

a) 0 1: 0 vs. : 0H H

b) 0 1: 0 vs. : 0H H

c) 0 1: 0 vs. : 0H r H r

d) 0 1: 0 vs. : 0H r H r

40. Referring to Table 2, to test whether the prison stocks portfolio is

negatively related to the S&P 500 index, the measured value of the

test statistic is

a) -7.019

b) -0.503

c) 0.072

d) 0.357

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41. Referring to Table 2, to test whether the prison stocks portfolio is

negatively related to the S&P 500 index, the p-value of the

associated test statistic is

a) 2.94942E-07

b) 2.94942E-07 / 2

c) 2.94942E-07 2

d) 8.7932E-13

42 Referring to Table 2, which of the following will be a correct

conclusion?

a) We cannot reject the null hypothesis and, therefore,

conclude that there is sufficient evidence to show that the

prisons stock portfolio and S&P 500 index are negatively

related.

b) We can reject the null hypothesis and, therefore, conclude

that there is sufficient evidence to show that the prisons stock

portfolio and S&P 500 index are negatively related.

c) We cannot reject the null hypothesis and, therefore,

conclude that there is not sufficient evidence to show that

the prisons stock portfolio and S&P 500 index are negatively

related.

d) We can reject the null hypothesis and conclude that there is

not sufficient evidence to show that the prisons stock portfolio

and S&P 500 index are negatively related.

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TABLE 3

It is believed that GPA (grade point average, based on a four point

scale) should have a positive linear relationship with ACT scores. Given

below is the Excel output from regressing GPA on ACT scores using a

data set of 8 randomly chosen students from a Big-Ten university.

Regressing GPA on ACT

Regression Statistics

Multiple R 0.7598

R Square 0.5774

Adjusted R

Square 0.5069

Standard Error 0.2691

Observations 8

ANOVA

df SS MS F

Significanc

e F

Regression 1 0.5940 0.5940 8.1986 0.0286

Residual 6 0.4347 0.0724

Total 7 1.0287

Coefficie

nts

Standard

Error t Stat P-value Lower 95% Upper 95%

Intercept 0.5681 0.9284 0.6119 0.5630 -1.7036 2.8398

ACT 0.1021 0.0356 2.8633 0.0286 0.0148 0.1895

43. Referring to Table 3, the interpretation of the coefficient of

determination in this regression is

a) 57.74% of the total variation of ACT scores can be explained

by GPA.

b) ACT scores account for 57.74% of the total fluctuation in

GPA.

c) GPA accounts for 57.74% of the variability of ACT scores.

d) None of the above.

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44. Referring to Table 3, the value of the measured test statistic to test

whether there is any linear relationship between GPA and ACT is

a) 0.0356

b) 0.1021

c) 0.7598

d) 2.8633

45. Referring to Table 3, what is the predicted average value of GPA

when ACT = 20?

a) 2.61

b) 2.66

c) 2.80

d) 3.12

46. Referring to Table 3, what are the decision and conclusion on

testing whether there is any linear relationship at 1% level of

significance between GPA and ACT scores?

a) Do not reject the null hypothesis; hence there is not sufficient

evidence to show that ACT scores and GPA are linearly

related.

b) Reject the null hypothesis; hence there is not sufficient

evidence to show that ACT scores and GPA are linearly

related.

c) Do not reject the null hypothesis; hence there is sufficient

evidence to show that ACT scores and GPA are linearly

related.

d) Reject the null hypothesis; hence there is sufficient evidence

to show that ACT scores and GPA are linearly related.

47. Referring to Table 3, the value of the measured (observed) test

statistic of the F-test for 0 1: 0 vs. : 0H H

a) may be negative.

b) is always positive.

c) is always negative.

d) has the same sign as the corresponding t test statistic.

48. True or False: A zero population correlation coefficient between a

pair of random variables means that there is no linear relationship

between the random variables.

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49. True or False: You give a pre-employment examination to your

applicants. The test is scored from 1 to 100. You have data on their

sales at the end of one year measured in dollars. You want to know

if there is any linear relationship between pre-employment

examination score and sales. An appropriate test to use is the t test

on the population correlation coefficient.

50. The width of the prediction interval for the predicted value of Y is

dependent on

a) the standard error of the estimate.

b) the value of X for which the prediction is being made.

c) the sample size.

d) All of the above.

END OF PAPER