Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. EE 1st Semester 70729 RESEARCH METHODOLOGY Question Paper.

Roll No. Total No. of Pages : 03

Total No. of Questions : 08

M.Tech. (EE)(2013 Onwards)/(Power System) (2013 & Onwards) (Sem.?1)

RESEARCH METHODOLOGY

Subject Code : MTRM-101

M.Code : 70729

Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE questions out of EIGHT questions.

2. Each question carries TWENTY marks.

1. Describe the important research design used in experimental hypoths is -testing research

study? (20)

2. a) Find the mean deviation from the mean for the following data : (10)

Class

interval

0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 8 12 10 8 3 2 7

b) In the frequency distribution of 100 families given below, the number of families

corresponding to expenditure groups 20 - 40 and 40 - 60 are missing from the table.

However, the median is known to be 50. Find the missing frequencies. (10)

Expenditure 0-20 20-40 40-60 60-80 80-100

No. of

families

14 ? 27 ? 15

3. a) Find the Karl Pearson's coefficient of correlation between x and y for the following

data : (10)

x 10 7 12 15 9 15 8

y 6 4 7 10 11 8 10

b) If the two lines of regression are 4x ? 5y + 30 = 0 and 20x ? 9y ?107 = 0. Which of

these is the line of regression of x on y and y on x. Find correlation coefficient and

standard deviation of y if the standard deviation of x is 3. (5)

c) The mean and S.D. of a sample of size 10 were found to be 9.5 and 2.5 respectively.

Later on an additional observation becomes available. This was 15.0 and was

included in the original sample. Find the mean. (5)

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1 | M-70729 (S9)-2484

Roll No. Total No. of Pages : 03

Total No. of Questions : 08

M.Tech. (EE)(2013 Onwards)/(Power System) (2013 & Onwards) (Sem.?1)

RESEARCH METHODOLOGY

Subject Code : MTRM-101

M.Code : 70729

Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE questions out of EIGHT questions.

2. Each question carries TWENTY marks.

1. Describe the important research design used in experimental hypoths is -testing research

study? (20)

2. a) Find the mean deviation from the mean for the following data : (10)

Class

interval

0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 8 12 10 8 3 2 7

b) In the frequency distribution of 100 families given below, the number of families

corresponding to expenditure groups 20 - 40 and 40 - 60 are missing from the table.

However, the median is known to be 50. Find the missing frequencies. (10)

Expenditure 0-20 20-40 40-60 60-80 80-100

No. of

families

14 ? 27 ? 15

3. a) Find the Karl Pearson's coefficient of correlation between x and y for the following

data : (10)

x 10 7 12 15 9 15 8

y 6 4 7 10 11 8 10

b) If the two lines of regression are 4x ? 5y + 30 = 0 and 20x ? 9y ?107 = 0. Which of

these is the line of regression of x on y and y on x. Find correlation coefficient and

standard deviation of y if the standard deviation of x is 3. (5)

c) The mean and S.D. of a sample of size 10 were found to be 9.5 and 2.5 respectively.

Later on an additional observation becomes available. This was 15.0 and was

included in the original sample. Find the mean. (5)

2 | M-70729 (S9)-2484

4. a) The theory predicts the proportion of beans, in the four groups A, B, C and D should

be 9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were

882,313, 287 and 118. Does the experimental result support the theory? (The table

value of

2

? for 3 d.f. at 5% level of significance is 7.81). (10)

b) Samples of sales in similar shops in two rooms are taken for a new product with the

following results : (10)

Town Mean sales Variance Size of samples

A 57 5.3 5

B 61 4.8 7

Is there any evidence of difference in sales in the two towns? Use 5% level of

significance for testing this difference between the mean of two samples. Use

t

10

(0.05) = 2.228

5. What do you understand by the Research proposal? Give the structure of Research

proposal. Enumerate the criteria for evaluating the Research proposal. (20)

6. a) A manufacturing company has purchased three new machines of different makes and

wishes to determine whether one of them is faster than the others in producing a

certain output. Five, hourly production figures are observed at random from each

machine and the results are given as below. (10)

Observations

Machine A Machine B Machine C

25 31 24

30 39 39

36 38 28

38 42 25

31 35 28

Use analysis of variance technique and determine whether the machines are significantly

different in their mean speed at the 5% level of significance. Given F

0.05

(2,12) =3.89

b) Complete the following randomized block design table. (10)

Source of

variations

d.f. Sum of

Squares (SS)

Mean sum of

squares (MSS)

F-ratio

Blocks 4 26.8 - -

Treatments 3 - - -

Error - - 2.5 -

Total - 85.3

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Roll No. Total No. of Pages : 03

Total No. of Questions : 08

M.Tech. (EE)(2013 Onwards)/(Power System) (2013 & Onwards) (Sem.?1)

RESEARCH METHODOLOGY

Subject Code : MTRM-101

M.Code : 70729

Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :

1. Attempt any FIVE questions out of EIGHT questions.

2. Each question carries TWENTY marks.

1. Describe the important research design used in experimental hypoths is -testing research

study? (20)

2. a) Find the mean deviation from the mean for the following data : (10)

Class

interval

0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 8 12 10 8 3 2 7

b) In the frequency distribution of 100 families given below, the number of families

corresponding to expenditure groups 20 - 40 and 40 - 60 are missing from the table.

However, the median is known to be 50. Find the missing frequencies. (10)

Expenditure 0-20 20-40 40-60 60-80 80-100

No. of

families

14 ? 27 ? 15

3. a) Find the Karl Pearson's coefficient of correlation between x and y for the following

data : (10)

x 10 7 12 15 9 15 8

y 6 4 7 10 11 8 10

b) If the two lines of regression are 4x ? 5y + 30 = 0 and 20x ? 9y ?107 = 0. Which of

these is the line of regression of x on y and y on x. Find correlation coefficient and

standard deviation of y if the standard deviation of x is 3. (5)

c) The mean and S.D. of a sample of size 10 were found to be 9.5 and 2.5 respectively.

Later on an additional observation becomes available. This was 15.0 and was

included in the original sample. Find the mean. (5)

2 | M-70729 (S9)-2484

4. a) The theory predicts the proportion of beans, in the four groups A, B, C and D should

be 9:3:3:1. In an experiment among 1600 beans, the numbers in the four groups were

882,313, 287 and 118. Does the experimental result support the theory? (The table

value of

2

? for 3 d.f. at 5% level of significance is 7.81). (10)

b) Samples of sales in similar shops in two rooms are taken for a new product with the

following results : (10)

Town Mean sales Variance Size of samples

A 57 5.3 5

B 61 4.8 7

Is there any evidence of difference in sales in the two towns? Use 5% level of

significance for testing this difference between the mean of two samples. Use

t

10

(0.05) = 2.228

5. What do you understand by the Research proposal? Give the structure of Research

proposal. Enumerate the criteria for evaluating the Research proposal. (20)

6. a) A manufacturing company has purchased three new machines of different makes and

wishes to determine whether one of them is faster than the others in producing a

certain output. Five, hourly production figures are observed at random from each

machine and the results are given as below. (10)

Observations

Machine A Machine B Machine C

25 31 24

30 39 39

36 38 28

38 42 25

31 35 28

Use analysis of variance technique and determine whether the machines are significantly

different in their mean speed at the 5% level of significance. Given F

0.05

(2,12) =3.89

b) Complete the following randomized block design table. (10)

Source of

variations

d.f. Sum of

Squares (SS)

Mean sum of

squares (MSS)

F-ratio

Blocks 4 26.8 - -

Treatments 3 - - -

Error - - 2.5 -

Total - 85.3

3 | M-70729 (S9)-2484

7. a) Suppose that the life length of the two bulbs B1 and B2 have distribution N(x; 40,36)

and N(x; 45, 9) respectively. If the bulb is to be used for 45-hour period, which bulb

is to be preferred? If it is to be used for 48-hour period, which bulb is to be preferred?

Given that P(Z<0.83)=0.7967, P(Z<1.33)=0.9082, P(Z<1.00) = 0.8143. (10)

b) Service calls come to a maintenance center, according to a Poisson process and, on

the average, 2.7 calls come per minute. Find the probability that : (10)

i) no more than 4 calls come in any minute

ii) fewer than 2 calls came in any minute

iii) more than 10 calls come in a 5-minute period

8. Discuss the basic requirement of report preparation, including report format, report

writing, graphs and tables. (20)

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any

page of Answer Sheet will lead to UMC against the Student.

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This post was last modified on 13 December 2019