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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)
4 of 14
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
6 of 14
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
7 of 14
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.
8 of 14
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.
10 of 14
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.
12 of 14
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