BA 9201 STATISTICS FOR MANAGEMENT JANUARY 2010 ANNA UNIVERSITY MBA QUESTION PAPER JANUARY 2010 REGULATION 2009
BA 9201 STATISTICS FOR MANAGEMENT JANUARY 2010 ANNA UNIVERSITY MBA QUESTION PAPER JANUARY 2010 REGULATION 2009
3. What is the central limit theorem?
4. What are elements and variables in a data set?
5. What are parametric tests?
6. If a class of students is examined and the researcher wants to test the
difference in performance between boys and girls, what test will you use?
7. What is a non parametric test?
8. Name four non parametric tests.
9. How will you test the accuracy of a regression equation?
10. Why are index numbers used?
200 employees at MNM, Inc.
Yearly Income Number
(In $1,000s) of Employees
20 – 24 2
25 – 29 48
30 – 34 60
35 – 39 80
40 – 44 10
(i) What percentage of employees has yearly income of $35,000 or
more?
(ii) Is the figure (percentage) that you computed in (i) an example of
statistical inference? If no, what kind of statistics does it represent?
(iii) Based on this sample, the president of the company said that ‘‘45%
of all our employees’ yearly income are $35,000 or more’’.
The president’s statement represents what kind of statistics?
(iv) With the statement made in (iii) can we assure that more than 45%
of all employees’ yearly income are at least $35,000? Explain.
(v) What percentage of employees of the sample has yearly income of
$29,000 or less?
(vi) How many variables are presented in the above data set?
(vii) The above data set represents the results of how many
observations?
Or
(b) An experiment consists of throwing two six–sided dice and observing the
number of spots on the upper faces. Determine the probability that
(i) the sum of the spots is 3
(ii) each die shows four or more spots
(iii) the sum of the spots is not 3
(iv) neither a one nor a six appear on each die
(v) a pair of sixes appear
(vi) the sum of the spots is 7.
12. (a) The life expectancy in the United States is 75 with a standard deviation
of 7 years. A random sample of 49 individuals is selected.
(i) What is the probability that the sample mean will be larger than 77
years?
(ii) What is the probability that the sample mean will be less than
72.7 years?
(iii) What is the probability that the sample mean will be between 73.5
and 76 years?
(iv) What is the probability that the sample mean will be between 72
and 74 years?
(v) What is the probability that the sample mean will be larger than
73.46 years?
Or
(b) A random sample of 121 checking accounts at a bank showed an average
daily balance of $280. The standard deviation of the population is known
to be $66.
(i) Is it necessary to know anything about the shape of the distribution
of the account balances in order to make an interval estimate of the
mean of all the account balances? Explain.
(ii) Find the standard error of the mean.
(iii) Give a point estimate of the population mean.
(iv) Construct a 80% confidence interval estimates for the mean.
(v) Construct a 95% confidence interval for the mean.
13. (a) The Dean of Students at UTC has said that the average grade of UTC
students is higher than that of the students at GSU. Random samples of
grades from the two schools are selected, and the results are shown
below.
UTC GSU
Sample Size 14 12
Sample Mean 2.85 2.61
Sample Standard Deviation 0.40 0.35
Sample Mode 2.5 3.0
(i) Give the hypotheses.
(ii) Compute the test statistic.
(iii) At a 0.1 level of significance, test the Dean of Students’ statement.
Or
(b) Random samples of employees from three different departments of NMC
Corporation showed the following yearly income (in $ 1,000).
Department A Department B Department C
40 46 46
37 41 40
43 43 41
41 33 48
35 41 39
38 42 44
At 05 . = α , test to determine if there is a significant difference among the
average income of the employees from the three departments. Use both
the critical and p- value approaches.
14. (a) The sales records of two branches of a department store over the last
12 months are shown below. (Sales figures are in thousands of dollars).
We want to use the Mann-Whitney-Willcoxon test to determine if there is
a significant difference in the sales of the two branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
Month Branch A Branch B
11 340 329
12 272 335
(i) Compute the sum of the ranks (T) for branch A.
(ii) Compute the mean T µ .
(iii) Compute T σ .
(iv) Use α= 0.05 and test to determine if there is a significant difference in
the populations of the sales of the two branches.
Or
(b) Two faculty members ranked 12 candidates for scholarships. Calculate
the Spearman rank-correlation coefficient and test it for significance. Use
0.02 level of significance.
Rank by Rank by
Candidate Professor A Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
15. (a) The following data represent the number of flash drives sold per day at a
local computer shop and their prices.
Price (x) Units Sold (y)
$34 3
36 4
32 6
35 5
30 9
38 2
40 1
(i) Develop a least-squares regression line and explain what the slope
of the line indicates.
(ii) Compute the coefficient of determination and comment on the
strength of relationship between x and y.
(iii) Compute the sample correlation coefficient between the price and
the number of flash drives sold. Use 01 . 0 = α to test the relationship
between x and y.
Or
(b) The table below gives the prices of four items —A, B, C and D— sold at a
store in 2000 and 2006
Price Price Quantity Quantity
Item 2000 2006 2000 2006
A $ 40 $ 10 1,000 800
B 55 25 1,900 5,000
C 95 40 600 3,000
D 250 90 50 200
(i) Using 2000 as the base year, calculate the price relative index for
the four items.
(ii) Calculate an unweighted aggregate price index for these items.
(iii) Find the Laspeyres weighted aggregate index for these items.
(iv) Find the Passche index for these items.
(v) Construct a weighted aggregate quantity index using 2000 as the
base year and price as the weight.
BA 9201 STATISTICS FOR MANAGEMENT JANUARY 2010 ANNA UNIVERSITY MBA QUESTION PAPER JANUARY 2010 REGULATION 2009
M.B.A. DEGREE EXAMINATION, JANUARY 2010
First Semester
BA 9201 — STATISTICS FOR MANAGEMENT
(Regulations 2009)
Time: Three hours Maximum: 100 Marks
Statistical Table Book need to be provided
Answer ALL Questions
PART A — (10 × 2 = 20 Marks)
1. What are the common types of variables used in statistics?
2. Name a few descriptive measures of data.3. What is the central limit theorem?
4. What are elements and variables in a data set?
5. What are parametric tests?
6. If a class of students is examined and the researcher wants to test the
difference in performance between boys and girls, what test will you use?
7. What is a non parametric test?
8. Name four non parametric tests.
9. How will you test the accuracy of a regression equation?
10. Why are index numbers used?
PART B — (5 × 16 = 80 Marks)
11. (a) The following data shows the yearly income distribution of a sample of200 employees at MNM, Inc.
Yearly Income Number
(In $1,000s) of Employees
20 – 24 2
25 – 29 48
30 – 34 60
35 – 39 80
40 – 44 10
(i) What percentage of employees has yearly income of $35,000 or
more?
(ii) Is the figure (percentage) that you computed in (i) an example of
statistical inference? If no, what kind of statistics does it represent?
(iii) Based on this sample, the president of the company said that ‘‘45%
of all our employees’ yearly income are $35,000 or more’’.
The president’s statement represents what kind of statistics?
(iv) With the statement made in (iii) can we assure that more than 45%
of all employees’ yearly income are at least $35,000? Explain.
(v) What percentage of employees of the sample has yearly income of
$29,000 or less?
(vi) How many variables are presented in the above data set?
(vii) The above data set represents the results of how many
observations?
Or
(b) An experiment consists of throwing two six–sided dice and observing the
number of spots on the upper faces. Determine the probability that
(i) the sum of the spots is 3
(ii) each die shows four or more spots
(iii) the sum of the spots is not 3
(iv) neither a one nor a six appear on each die
(v) a pair of sixes appear
(vi) the sum of the spots is 7.
12. (a) The life expectancy in the United States is 75 with a standard deviation
of 7 years. A random sample of 49 individuals is selected.
(i) What is the probability that the sample mean will be larger than 77
years?
(ii) What is the probability that the sample mean will be less than
72.7 years?
(iii) What is the probability that the sample mean will be between 73.5
and 76 years?
(iv) What is the probability that the sample mean will be between 72
and 74 years?
(v) What is the probability that the sample mean will be larger than
73.46 years?
Or
(b) A random sample of 121 checking accounts at a bank showed an average
daily balance of $280. The standard deviation of the population is known
to be $66.
(i) Is it necessary to know anything about the shape of the distribution
of the account balances in order to make an interval estimate of the
mean of all the account balances? Explain.
(ii) Find the standard error of the mean.
(iii) Give a point estimate of the population mean.
(iv) Construct a 80% confidence interval estimates for the mean.
(v) Construct a 95% confidence interval for the mean.
13. (a) The Dean of Students at UTC has said that the average grade of UTC
students is higher than that of the students at GSU. Random samples of
grades from the two schools are selected, and the results are shown
below.
UTC GSU
Sample Size 14 12
Sample Mean 2.85 2.61
Sample Standard Deviation 0.40 0.35
Sample Mode 2.5 3.0
(i) Give the hypotheses.
(ii) Compute the test statistic.
(iii) At a 0.1 level of significance, test the Dean of Students’ statement.
Or
(b) Random samples of employees from three different departments of NMC
Corporation showed the following yearly income (in $ 1,000).
Department A Department B Department C
40 46 46
37 41 40
43 43 41
41 33 48
35 41 39
38 42 44
At 05 . = α , test to determine if there is a significant difference among the
average income of the employees from the three departments. Use both
the critical and p- value approaches.
14. (a) The sales records of two branches of a department store over the last
12 months are shown below. (Sales figures are in thousands of dollars).
We want to use the Mann-Whitney-Willcoxon test to determine if there is
a significant difference in the sales of the two branches.
Month Branch A Branch B
1 257 210
2 280 230
3 200 250
4 250 260
5 284 275
6 295 300
7 297 320
8 265 290
9 330 310
10 350 325
Month Branch A Branch B
11 340 329
12 272 335
(i) Compute the sum of the ranks (T) for branch A.
(ii) Compute the mean T µ .
(iii) Compute T σ .
(iv) Use α= 0.05 and test to determine if there is a significant difference in
the populations of the sales of the two branches.
Or
(b) Two faculty members ranked 12 candidates for scholarships. Calculate
the Spearman rank-correlation coefficient and test it for significance. Use
0.02 level of significance.
Rank by Rank by
Candidate Professor A Professor B
1 6 5
2 10 11
3 2 6
4 1 3
5 5 4
6 11 12
7 4 2
8 3 1
9 7 7
10 12 10
11 9 8
12 8 9
15. (a) The following data represent the number of flash drives sold per day at a
local computer shop and their prices.
Price (x) Units Sold (y)
$34 3
36 4
32 6
35 5
30 9
38 2
40 1
(i) Develop a least-squares regression line and explain what the slope
of the line indicates.
(ii) Compute the coefficient of determination and comment on the
strength of relationship between x and y.
(iii) Compute the sample correlation coefficient between the price and
the number of flash drives sold. Use 01 . 0 = α to test the relationship
between x and y.
Or
(b) The table below gives the prices of four items —A, B, C and D— sold at a
store in 2000 and 2006
Price Price Quantity Quantity
Item 2000 2006 2000 2006
A $ 40 $ 10 1,000 800
B 55 25 1,900 5,000
C 95 40 600 3,000
D 250 90 50 200
(i) Using 2000 as the base year, calculate the price relative index for
the four items.
(ii) Calculate an unweighted aggregate price index for these items.
(iii) Find the Laspeyres weighted aggregate index for these items.
(iv) Find the Passche index for these items.
(v) Construct a weighted aggregate quantity index using 2000 as the
base year and price as the weight.
