BA 9201 STATISTICS FOR MANAGEMENT JUNE 2010 ANNA UNIVERSITY MBA QUESTION PAPER JUNE 2010 REGULATION 2009
3. What is a sampling distribution?
4. Give two rules for determining sample size.
5. What is a hypothesis?
6. What is meant by design of experiments?
7. What is a non-parametric test?
8. When is Kruskal-Wallis test used?
9. When is regression used?
10. What is an index number?
PART B — (5 × 16 = 80 Marks)
11. (a) The following information regarding the top ten Fortune 500 companies was presented
in an issue of Fortune Magazine.
Company Sales
$ Millions
Sales
Rank
Profits
$ Millions
Profits
Rank
General Motors 161,315 1 2,956 30
Ford Motor 144,416 2 22,071 2
Wal-Mart Stores 139,208 3 4,430 14
Exxon 100,697 4 6,370 5
General Electric 100,469 5 9,269 3
Int'l Business Machines 81,667 6 6,328 6
Citigroup 76,431 7 5,807 8
Philip Morris 57,813 8 5,372 9
Boeing 56,154 9 1,120 82
AT and T 53,588 10 6,398 4
(i) How many elements are in the above data set?
(ii) How many variables are in this data set?
(iii) How many observations are in this data set?
(iv) Which variables are qualitative and which are quantitative variables?
(v) What measurement scale is used for each variable?
Or
(b) In the two upcoming basketball games (involving A & B and A & C), the probability
that A will defeat B is 0.63, and the probability that A will defeat C is 0.55. The
probability that A will defeat both opponents is 0.3465.
(i) What is the probability that A will defeat C given that they defeat B?
(ii) What is the probability that A will win at least one of the games?
(iii) What is the probability of A winning both games?
(iv) Are the outcomes of the games independent? Explain and substantiate your
answer.
12. (a) The values obtained from a random sample of 4 observations taken from an infinite
population are given below:
32, 34, 35, 39
(i) Find a point estimate for . µ Is this an unbiased estimate of µ? Explain.
(ii) Find a point estimate for 2
σ . Is this an unbiased estimated of 2
σ ? Explain.
(iii) Find a point estimate for . σ
(iv) What can be said about the sampling distribution of x ? Discuss the expected
value, the standard deviation, and the shape of the sampling distribution of x .
Or
(b) A bank has kept records of the checking balances of its customers and determined that
the average daily balance of its customers is $300 with a standard deviation of $48. A
random sample of 144 checking accounts is selected.
(i) What is probability that the sample mean will be more than $306.60?
(ii) What is probability that the sample mean will be less than $308?
(iii) What is probability that the sample mean will be between $302 and $308?
(iv) What is the probability that the sample mean will be at least $296?
13. (a) The following is the information obtained from a random sample of 5 observations.
Assume the population has a normal distribution.
20, 18, 17, 22, 18
It is required to determine whether or not the mean of the population from which this
sample was taken is significantly less than 21
(i) State the null and the alternative hypotheses.
(ii) Compute the standard error of the mean.
(iii) Determine the test statistic.
(iv) Determine the − p value and at 90% confidence, test whether or not the mean of
the population is significantly less than 21.
Or
(b) In order to test to see if there is any significant difference in the mean number of units
produced per week by each of three production methods, the following data were
collected. (Note that the sample sizes are not equal.)
Method I Method II Method III
182 170 162
170 192 166
179 190
(i) Compute x .
(ii) At the α= 0.05 level of significance, is there any difference in the mean number of
units produced per week by each method? Show the complete ANOVA table. Use
both the critical and p -value approaches.
14. (a) Independent random samples of ten day students and ten evening students at a
University showed the following age distributions. We want to use the Mann-Whitney-
Wilcoxon test to determine if there is a significant difference in the age distribution of
the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks (T) for the day students.
(ii) Compute the mean . T µ
(iii) Compute . T σ
(iv) Use 05 . 0 = α and test for any significant differences in the age distribution of the
two populations.
Or
(b) In a sample of 400 people, 250 indicated that they prefer domestic products, while 140
said they prefer foreign products, and 10 indicated no preference. We want to use the
sign test to determine if there is evidence of a significant difference in the preferences
for the two types of products.
(i) Provide the hypotheses to be tested.
(ii) Compute the mean.
(iii) Compute the standard deviation.
132 132 132
J6501 4
(iv) At 95% confidence, test to determine if there is evidence of a significant difference
in the preferences for the two types of products.
15. (a) A coffee shop owner believes that the sales of coffee at his coffee shop depend upon the
weather. He has taken a sample of 6 days. The results of the sample are given below.
Cups of Coffee Sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
(i) Which variable is the dependent variable?
(ii) Compute the least square estimated line.
(iii) Compute the correlation coefficient between temperature and the sales of coffee.
(iv) Predict sales of a 90 degree day.
Or
(b) The table below gives the prices of four items – A, B, C and D – sold at a store in 2000
and 2006.
Item Price
2000
$
Price
2006
$
Quantity
2000
Quantity
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 Lasperyres’s weighted aggregate index for these items.
(iv) Find the Paasche index for these items.
(v) Construct a weighted aggregate quantity index using 2000 as the base year price
as the weight.
M.B.A. DEGREE EXAMINATION, JUNE 2010
First Semester
BA9201 — STATISTICS FOR MANAGEMENT
(Regulation 2009)
Time : Three hours Maximum : 100 Marks
Statistical Table Book need to be provided
Answer ALL Questions
PART A — (10 × 2 = 20 Marks)
1. Distinguish between qualitative and quantitative variables in statistics.
2. Name four descriptive statistics used.3. What is a sampling distribution?
4. Give two rules for determining sample size.
5. What is a hypothesis?
6. What is meant by design of experiments?
7. What is a non-parametric test?
8. When is Kruskal-Wallis test used?
9. When is regression used?
10. What is an index number?
PART B — (5 × 16 = 80 Marks)
11. (a) The following information regarding the top ten Fortune 500 companies was presented
in an issue of Fortune Magazine.
Company Sales
$ Millions
Sales
Rank
Profits
$ Millions
Profits
Rank
General Motors 161,315 1 2,956 30
Ford Motor 144,416 2 22,071 2
Wal-Mart Stores 139,208 3 4,430 14
Exxon 100,697 4 6,370 5
General Electric 100,469 5 9,269 3
Int'l Business Machines 81,667 6 6,328 6
Citigroup 76,431 7 5,807 8
Philip Morris 57,813 8 5,372 9
Boeing 56,154 9 1,120 82
AT and T 53,588 10 6,398 4
(i) How many elements are in the above data set?
(ii) How many variables are in this data set?
(iii) How many observations are in this data set?
(iv) Which variables are qualitative and which are quantitative variables?
(v) What measurement scale is used for each variable?
Or
(b) In the two upcoming basketball games (involving A & B and A & C), the probability
that A will defeat B is 0.63, and the probability that A will defeat C is 0.55. The
probability that A will defeat both opponents is 0.3465.
(i) What is the probability that A will defeat C given that they defeat B?
(ii) What is the probability that A will win at least one of the games?
(iii) What is the probability of A winning both games?
(iv) Are the outcomes of the games independent? Explain and substantiate your
answer.
12. (a) The values obtained from a random sample of 4 observations taken from an infinite
population are given below:
32, 34, 35, 39
(i) Find a point estimate for . µ Is this an unbiased estimate of µ? Explain.
(ii) Find a point estimate for 2
σ . Is this an unbiased estimated of 2
σ ? Explain.
(iii) Find a point estimate for . σ
(iv) What can be said about the sampling distribution of x ? Discuss the expected
value, the standard deviation, and the shape of the sampling distribution of x .
Or
(b) A bank has kept records of the checking balances of its customers and determined that
the average daily balance of its customers is $300 with a standard deviation of $48. A
random sample of 144 checking accounts is selected.
(i) What is probability that the sample mean will be more than $306.60?
(ii) What is probability that the sample mean will be less than $308?
(iii) What is probability that the sample mean will be between $302 and $308?
(iv) What is the probability that the sample mean will be at least $296?
13. (a) The following is the information obtained from a random sample of 5 observations.
Assume the population has a normal distribution.
20, 18, 17, 22, 18
It is required to determine whether or not the mean of the population from which this
sample was taken is significantly less than 21
(i) State the null and the alternative hypotheses.
(ii) Compute the standard error of the mean.
(iii) Determine the test statistic.
(iv) Determine the − p value and at 90% confidence, test whether or not the mean of
the population is significantly less than 21.
Or
(b) In order to test to see if there is any significant difference in the mean number of units
produced per week by each of three production methods, the following data were
collected. (Note that the sample sizes are not equal.)
Method I Method II Method III
182 170 162
170 192 166
179 190
(i) Compute x .
(ii) At the α= 0.05 level of significance, is there any difference in the mean number of
units produced per week by each method? Show the complete ANOVA table. Use
both the critical and p -value approaches.
14. (a) Independent random samples of ten day students and ten evening students at a
University showed the following age distributions. We want to use the Mann-Whitney-
Wilcoxon test to determine if there is a significant difference in the age distribution of
the two groups.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 39
33 45
31 35
(i) Compute the sum of the ranks (T) for the day students.
(ii) Compute the mean . T µ
(iii) Compute . T σ
(iv) Use 05 . 0 = α and test for any significant differences in the age distribution of the
two populations.
Or
(b) In a sample of 400 people, 250 indicated that they prefer domestic products, while 140
said they prefer foreign products, and 10 indicated no preference. We want to use the
sign test to determine if there is evidence of a significant difference in the preferences
for the two types of products.
(i) Provide the hypotheses to be tested.
(ii) Compute the mean.
(iii) Compute the standard deviation.
132 132 132
J6501 4
(iv) At 95% confidence, test to determine if there is evidence of a significant difference
in the preferences for the two types of products.
15. (a) A coffee shop owner believes that the sales of coffee at his coffee shop depend upon the
weather. He has taken a sample of 6 days. The results of the sample are given below.
Cups of Coffee Sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
(i) Which variable is the dependent variable?
(ii) Compute the least square estimated line.
(iii) Compute the correlation coefficient between temperature and the sales of coffee.
(iv) Predict sales of a 90 degree day.
Or
(b) The table below gives the prices of four items – A, B, C and D – sold at a store in 2000
and 2006.
Item Price
2000
$
Price
2006
$
Quantity
2000
Quantity
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 Lasperyres’s weighted aggregate index for these items.
(iv) Find the Paasche index for these items.
(v) Construct a weighted aggregate quantity index using 2000 as the base year price
as the weight.
