Anna University Previous Years Question Papers
Question paper code: 40201
M.B.A. DEGREE EXAMINATION,APRIL/MAY-2015
First semester
BA 9201/BA911/UBA9101/10488 MB 102-STATISTICS FOR MANAGEMENT
(Regulation 2008/2010)
Time- Three hour
Maximum mark-100
Answer all questions
PART A-10X2=20
1. What are the common types of variables used in statistics?
2. Name a few descriptive measures of data.
3. State central limit theorem.
4. What are the property of an estimator?
5. What is a hypothesis?
6. What is meant by design of experiments?
7. Write the meaning of non-parametric test?
8. How do you find the degrees of freedom in case of chi-square test?
9. Define seasonal variations and cyclic variations.
10. Explain briefly about the Laspeyre’s method of constructing index number.
PART B-5X16=80MARKS
11.(a) The following data show the yearly income distribution of a sample of 200 employees at MNM, inc.
Yearly income Number of
(In $1,000s) 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 statistical does it represent?
(iii) Based on this sample, the president of the company side that “45% of all our employees’ yearly income are $35,000 or more”. The president’ statement represent what kind of statistics?
(iv) With the statement mate 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 consist 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 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 six appear
(vi)the sum of the spots is 7
12.(a)(i) Find the probability that in 120 tosses of a fair coin (1) between 40%and 60% will be heads (2)5/8 or more will be heads.
(ii) A population consists of five number 2,3,6,8,11. Consist all possible sample of size to which can be drawn with replacement from this population. Find the mean of the sampling distribution of means , the standard deviation of the sampling distribution of means.
(or)
(b)(i)Suppose that the heights of 100 male students at XYZ university represented a random sample of the highest of all male student at the university. Find (1)95% (2)99% confidents intervals for estimating the means height of the XYZ university students.
(ii)A sample of five measurement of a diameter of a sphere were record by a scientist as 6.33,6.37, 6.36 , 6.32 and 6.37 cm. Determine unbiased and efficient estimates of 1 the true mean (2) the turn variance. Assume that the measured diameter is normally distributed.
13.(a) The average number of defective articles in a certain factory is claimed to be less than the average for all the factories. The average for all the factories is 30.5. A random sample of 100 defective articles showed the following distribution.
Class limits: 16-20 21-25 26-30 31-35 36-40
Number: 12 22 20 30 16
Calculate the mean and the standard deviation of the sample and use it to test the claim that the average is less than the figure for all the factories at 5% level of significance. Given Z(-1.645)=0.95.
(or)
(b)Three samples below have been obtained from the normal population with equal variance. Test the hypothesis that the sample means are equal.
I II III
8 7 12
10 5 9
7 10 13
14 9 12
11 9 14
14.(a)Independent random sample of ten day students and ten evening students at a university showed a 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 group.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 29
33 45
31 35
(i) Compute the sum of rank (T)for the day student
(ii) Compute the mean µt
(iii) Compute σt
(iv) Use α=0.05and test for any significant difference in the age distribution of the two population.
(or)
(b)In a sample of 400 people 250 indicated that day 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 two types of products.
(i) Provide the hypotheses
(ii)Compute the mean
(iii)Compute the standard deviation
(iv)At 95% confidents test to determine if there is evidence of a significant difference in the preferences of the two types of products.
15.(a) Estimate the pearson correlation coefficient by using the following data:
Job: 1 2 3 4 5 6 7 8 9 10
Systems1:4.1 5.0 4.9 5.3 13.5 12.0 19.2 10.0 24.1 6.9
Systems2:3.9 5.1 5.0 4.9 13.3 13.2 21.3 9.1 23.0 8.1
(or)
(b)Compute seasonal variations from the following time series using moving average method
Year 2002 2003 2004 2005
Quarter
Q1 75 86 90 100
Q2 60 65 70 72
Q3 54 63 66 72
Q4 59 80 85 93
Question paper code: 40201
M.B.A. DEGREE EXAMINATION,APRIL/MAY-2015
First semester
BA 9201/BA911/UBA9101/10488 MB 102-STATISTICS FOR MANAGEMENT
(Regulation 2008/2010)
Time- Three hour
Maximum mark-100
Answer all questions
PART A-10X2=20
1. What are the common types of variables used in statistics?
2. Name a few descriptive measures of data.
3. State central limit theorem.
4. What are the property of an estimator?
5. What is a hypothesis?
6. What is meant by design of experiments?
7. Write the meaning of non-parametric test?
8. How do you find the degrees of freedom in case of chi-square test?
9. Define seasonal variations and cyclic variations.
10. Explain briefly about the Laspeyre’s method of constructing index number.
PART B-5X16=80MARKS
11.(a) The following data show the yearly income distribution of a sample of 200 employees at MNM, inc.
Yearly income Number of
(In $1,000s) 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 statistical does it represent?
(iii) Based on this sample, the president of the company side that “45% of all our employees’ yearly income are $35,000 or more”. The president’ statement represent what kind of statistics?
(iv) With the statement mate 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 consist 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 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 six appear
(vi)the sum of the spots is 7
12.(a)(i) Find the probability that in 120 tosses of a fair coin (1) between 40%and 60% will be heads (2)5/8 or more will be heads.
(ii) A population consists of five number 2,3,6,8,11. Consist all possible sample of size to which can be drawn with replacement from this population. Find the mean of the sampling distribution of means , the standard deviation of the sampling distribution of means.
(or)
(b)(i)Suppose that the heights of 100 male students at XYZ university represented a random sample of the highest of all male student at the university. Find (1)95% (2)99% confidents intervals for estimating the means height of the XYZ university students.
(ii)A sample of five measurement of a diameter of a sphere were record by a scientist as 6.33,6.37, 6.36 , 6.32 and 6.37 cm. Determine unbiased and efficient estimates of 1 the true mean (2) the turn variance. Assume that the measured diameter is normally distributed.
13.(a) The average number of defective articles in a certain factory is claimed to be less than the average for all the factories. The average for all the factories is 30.5. A random sample of 100 defective articles showed the following distribution.
Class limits: 16-20 21-25 26-30 31-35 36-40
Number: 12 22 20 30 16
Calculate the mean and the standard deviation of the sample and use it to test the claim that the average is less than the figure for all the factories at 5% level of significance. Given Z(-1.645)=0.95.
(or)
(b)Three samples below have been obtained from the normal population with equal variance. Test the hypothesis that the sample means are equal.
I II III
8 7 12
10 5 9
7 10 13
14 9 12
11 9 14
14.(a)Independent random sample of ten day students and ten evening students at a university showed a 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 group.
Day Evening
26 32
18 24
25 23
27 30
19 40
30 41
34 42
21 29
33 45
31 35
(i) Compute the sum of rank (T)for the day student
(ii) Compute the mean µt
(iii) Compute σt
(iv) Use α=0.05and test for any significant difference in the age distribution of the two population.
(or)
(b)In a sample of 400 people 250 indicated that day 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 two types of products.
(i) Provide the hypotheses
(ii)Compute the mean
(iii)Compute the standard deviation
(iv)At 95% confidents test to determine if there is evidence of a significant difference in the preferences of the two types of products.
15.(a) Estimate the pearson correlation coefficient by using the following data:
Job: 1 2 3 4 5 6 7 8 9 10
Systems1:4.1 5.0 4.9 5.3 13.5 12.0 19.2 10.0 24.1 6.9
Systems2:3.9 5.1 5.0 4.9 13.3 13.2 21.3 9.1 23.0 8.1
(or)
(b)Compute seasonal variations from the following time series using moving average method
Year 2002 2003 2004 2005
Quarter
Q1 75 86 90 100
Q2 60 65 70 72
Q3 54 63 66 72
Q4 59 80 85 93
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