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Bmgt 220-Business Statistics Ii 2010 Question Paper
Bmgt 220-Business Statistics Ii 2010
Course:Bachelor Of Commerce
Institution: Kabarak University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS
2009/2010 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF COMMERCE
COURSE CODE: BMGT 220
COURSE TITLE: BUSINESS STATISTICS II
STREAM: Y2S2
INSTRUCTIONS:
• Answer question One and any other Two Questions
QUESTION ONE
1. a) Explain the meaning of the following terms:
I. population
II. sample
III. parameter
IV. statistic
V. variable
VI. sample error (3marks)
b) Given N~(75,5),
I. illustrate the wanted area on a normal curve (2marks)
II. find P(x>82) (3marks)
c) What is a binomial distribution (1marks)
I. According to the journal of higher education, 40% of all high school graduates
work during the summer to earn for college tuition for the upcoming fall term.
If 18 graduates are selected at random, what is the probability that none work
(3 marks)
II. What is the meaning of your result (1 mark)
d) Your statistics professor has given five tests this semester .You scored 70,65,75,80,95
for a mean of µ= 77. He decides to determine your grade by randomly selecting a
sample of three test scores. Construct the sampling distribution for this process. What
observations might you make? (4marks)
e) Differentiate between type I and type II errors (2marks)
f) In trying to model a set of data in Minitab, a statistician input the following linear
regression model Y = a +?x + e. From this model what represents the following:
i) Regression coefficient
ii) Regression constant
iii) Error term
iv) Dependent term
v) Independent term (5 marks)
g) In Alphax college there is a population of N = 4 incomes for four college students.
Theses incomes are; shs.100, shs200, shs300, and shs400. If a sample of n = 2
observations is selected to estimate the mean, four samples are observed to result in
some error. Estimate the standard error of the sampling distribution. What do you
conclude? (5 marks)
[TOTAL 30 MARKS]
QUESTION TWO
a) Business Week has reported that fiscal earnings for Playboy Enterprises, Inc. have
shown significant reductions in the last few years. Christine Hefner, the founder’s
daughter, assumed the position of CEO Playboy in November 1988. Ms. Hefner has
found the mean monthly revenues for the various Playboy clubs around the nation are
$1.23 million with a standard deviation of $0.65 million. Assume for the moment a
normality in the distribution of monthly earnings.
If the revenues for the month were selected for any of the clubs, what is the
probability it would:
i) Exceed $1.3 million? (2marks)
ii) Be between $1.5 million and $2.0 million? (2marks)
b) Last March, one of the clubs reported revenues of $0.89 million ($890,000). In
response to Ms. Hefner’s displeasure, the manager of that particular club offered the
defense that revenues that low were not unusual. How would you respond to such a
defense? (2 marks)
c) If Ms. Hefner wishes to single out for corrective actions those clubs reporting receipts
in the lowest 12 percent, what level of revenues must a club exceed without receiving
this undesirable attention? (2 marks)
d) Assume that over the course of an entire year, St. Jude’s Hospital admitted 50 patients
who must be examined to determine if they might require surgery. What is the
probability that more than one-half will require surgery? Records show that
traditionally, 40 percent of their patients must submit to surgery. (2 marks)
e) What is Poisson distribution? (1 mark)
f) St. Andrew’s Hospital has reported that an average of 7.2 patients arrive in the
emergency room each hour. The hospital administrator wants to know the probability
that;
(i) Exactly 10 patients arrive in any given hour (3 marks)
(ii) The probability the number of arrivals will exceed emergency room capacity,
which is for 15 patients. (3 marks)
(iii) State any three probability distributions. (3 marks)
[TOTAL 20 MARKS]
QUESTION THREE
(a) Explain the various steps involved in hypothesis testing. (10 marks)
(b) The Noah face company feels that the average number of days required to complete a
job is µ=27. Fifty jobs are randomly selected in order to test the assertion. The mean
is found to be =25.3 days, with a standard deviation of d=2.1 days. Mr. Noah
wishes to test the hypothesis at the 1 percent level of significance (99 percent of
confidence). State the set of hypothesis and run the test. (8 marks)
(c) Explain the characteristics of t-distribution (2 marks)
QUESTION FOUR
(a) The management of Hop Scotch Airlines, the world’s smallest air carrier, assumes a
direct relationship between advertising and the number of passengers who choose to
fly Hop Scotch. To determine if this relationship does exist and, if so, what its exact
nature might be, the statisticians employed by Hop Scotch set out to use OLS
procedures to determine the registration model.
Observation
(months)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Advertising (in
$1,000’s) (X)
10 12 8 17 10 15 10 14 19 10 11 13 16 10 12
Passengers (in
1,000’s) ) (Y)
15 17 13 23 16 21 14 20 24 17 16 18 22 15 16
i) Calculate the least square regression line. (8 marks)
ii) Interpret the results. (2 marks)
(b) 1. Given the above data obtain the coefficient of determination. (4 marks)
2. What is your statistical interpretation? (2 marks)
3. Is it correct to state the number of passengers is caused by changes in advertising
expenditure? (2 marks)
4. Obtain Karl Pearson’s product moment correlation. (2 marks)
[TOTAL 20 MARKS]
QUESTION FIVE
(a) The U.S and Wildlife Service tagged salmon spawning in the Hood River near
Seattle to determine migration patterns. The service felt that 40 percent of the fish
returned there each year.
i. If a sample of 2,022 revealed 822 had been tagged the previous year, is the
service’s hypothesis supported at the 5 percent level? (2 marks)
ii. Calculate the p-value associated with the findings. (2 marks)
iii. Calculate the probability of a Type II error if the true proportion is 0.38.
(2 marks)
(b) Assume that industry records show that 10 percent of the employees steal from their
employers. The personnel manager of a firm in that industry wishes to determine the
probability that from a sample of 20 employees, 3 have illegally taken company
property. Estimate this probability using both Binomial and Poisson distribution.
(6 marks)
(c) Parker Seal, Inc. makes O-rings for NASA’s space shuttle. The rings are designed to
seal connections and joint fittings in the fuel system to prevent leaks. One type of ring
must be 5 centimeters in diameter in order to fit property. It can vary up or down by only
0.25 centimeter without causing a dangerous leak. Parker Seal claims that this ring
averages 5 centimeters, with a standard deviation of 0.17 centimeter. If these figures are
correct and a normal distribution in diameters is assumed, determine;
i. The proportions of rings that will fit properly. (3 marks)
ii. The proportion of rings that are defective. (3 marks)
iii. The probability any one ring has a diameter greater than 5.3
centimeters (3 marks)
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