IGNOU MSTL-001 Solved Assignment 2023 | IGNOU PGDAST.gif

IGNOU MSTL-001 Solved Assignment 2023 | PGDAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

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IGNOU MSTL-001 Assignment Question Paper 2023

Course Code: MSTL-001

Assignment Code: MSTL-001/TMA/2023

Maximum Marks: 100

\section{Note:}

1. All questions are compulsory.

2. Solve the following questions in MS Excel.

3. Take the screenshots of the final output/spreadsheet.

4. Paste all screenshots in the assignment booklets with all necessary interpretation and steps.

Q 1 A cooking oil supplier distributed two types of oils, say Oil A and Oil B to a large numbers of retail stores. The supplier wants to compare the popularity of both oils. For this purpose, he selects a sample of 100 stores and tracks record of the sold oils (in litres) of each type at each store. The data are noted in the following table:

Store No.

Oil A

Oil B

Store No.

Oil A

Oil B

1

161

419

51

478

196

2

285

411

52

284

241

3

219

168

53

488

182

4

321

241

54

447

132

5

435

125

55

384

322

6

325

261

56

267

341

7

463

119

57

390

139

8

319

285

58

270

462

9

108

441

59

381

227

10

328

213

60

252

140

11

479

116

61

245

420

12

285

319

62

196

474

13

489

135

63

201

392

14

448

187

64

227

452

15

385

349

65

181

406

16

268

279

66

441

397

17

391

306

67

130

375

18

271

296

68

213

455

19

382

269

69

373

367

20

253

403

70

190

503

21

246

309

71

280

366

22

197

424

72

236

486

23

202

349

73

297

171

24

228

250

74

421

219

25

182

457

75

340

173

26

442

196

76

380

418

27

131

240

77

308

454

28

214

337

78

361

228

29

374

252

79

183

432

30

191

423

80

121

468

31

281

322

81

162

231

32

237

406

82

286

252

33

298

146

83

220

283

34

422

175

84

322

114

35

341

487

85

436

325

36

381

278

86

326

213

37

309

442

87

464

229

38

362

326

88

320

183

39

184

414

89

120

291

40

122

377

90

329

175

41

160

250

91

480

141

42

284

272

92

286

394

43

218

356

93

490

163

44

320

366

94

449

134

45

434

170

95

386

130

46

324

213

96

134

459

47

462

147

97

392

363

48

318

195

98

272

315

49

118

452

99

383

338

50

327

385

100

254

365

Answer the following:

i) Which type of oil has more average sales?

ii) Which oil shows greater variability in the sales?

iii) Determine the correlation between both types of oils.

iv) Compute suitable width of the class intervals for both oils,

v) Construct the continuous frequency distribution for both oils.

Q 2 The scores (out of 100) secured by 60 employees of three different departments D1, D2 and D3 who participated in a study, are presented in the following table:

Employee No.

Scores of D1

Scores of D2

Scores of D3

Employee No.

Scores of D1

Scores of D2

Scores of D3

1

54

78

56

31

59

76

57

2

49

73

55

32

57

87

66

3

36

72

52

33

46

80

62

4

64

87

67

34

57

82

61

5

47

85

65

35

48

78

59

6

46

75

58

36

65

90

66

7

61

94

70

37

69

94

70

8

56

88

67

38

43

73

54

9

57

81

59

39

36

68

48

10

43

73

56

40

43

66

48

11

60

89

69

41

56

90

66

12

54

92

70

42

52

73

56

13

56

96

75

43

57

83

61

14

55

85

62

44

45

69

51

15

53

89

66

45

46

75

58

16

63

85

64

46

58

88

64

17

50

67

47

47

49

73

53

18

67

96

71

48

60

92

68

19

50

67

49

49

63

81

59

20

54

87

64

50

51

78

57

21

41

69

49

51

53

76

58

22

53

83

60

52

47

76

56

23

55

85

64

53

38

68

52

24

58

76

59

54

46

82

63

25

36

70

54

55

39

66

47

26

49

71

51

56

67

91

71

27

62

95

74

57

61

82

61

28

66

88

65

58

56

83

60

29

53

75

56

59

48

67

50

30

49

88

64

60

35

68

50

i) Compute the correlation coefficient between scores of the employees working in department D1 and the joint effects of scores of the employees of departments D1 and D2.

ii) Compute the correlation coefficient between scores of the employees working in departments D1 and D2 after eliminating the linear effect of the scores of departments D3.

iii) Also represent the scores obtained by departments D1, D2 and D3 using box plot.

 

Q3 An experiment was conducted to compare two metals: A and B, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the pressures required for breaking the metal are given in the following table:

S. No.

Breaking Pressure

 

S. No.

Breaking Pressure

 
 

Metal A

Metal B

 

Metal A

Metal B

1

71.9

72.2

21

86.5

70.6

2

68.8

66.4

22

74.3

74.6

3

82.6

74.5

23

71.2

68.8

4

78.1

60.6

24

85

76.9

5

74.2

73.2

25

80.5

63

6

70.8

68.7

26

76.6

75.6

7

84.9

69

27

73.2

71.1

8

72.7

73

28

87.3

71.4

9

69.6

67.2

29

75.1

75.4

10

83.4

75.3

30

72

69.6

11

78.9

61.4

31

85.8

77.3

12

75

74

32

81.3

63.4

13

71.6

69.5

33

77.4

76

14

85.7

69.8

34

74

71.5

15

73.5

73.8

35

88.1

71.8

16

70.4

68

36

75.9

75.8

17

84.2

76.1

37

72.8

70

18

79.7

62.2

38

86.6

77.7

19

75.8

74.8

39

82.1

63.8

20

72.4

70.3

40

78.2

76.4

If the pressure required to break both metals are normally distributed, then answers the following questions:

i) Are the variances of the distributions of the pressure of Metals A and B equal at \(5 \%\) level of significance?

ii) If yes, check whether the average pressure for Metal \(\mathrm{A}\) is more than the Metal \(\mathrm{B}\) at \(5 \%\) level of significance?

Q 4 An investigation was performed to study the impacts of different types of machines on the production of a particular variety of toys. The six machines \((\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and F) are assigned at random to 36 cells of the square with the restriction that each machine is used only once by each operator and in each time-period. The following design was obtained in which 6 operators are arranged in “columns” and 6 time-periods are in “rows”:

   

Operator

       
   

1

 

2

3

 

4

5

6

Time Period

1

 

A

 

B

C

 

D

E

F

 

2

 

B

 

C

D

 

E

F

A

 

3

 

C

 

D

E

 

F

A

B

 

4

 

D

 

E

F

 

A

B

C

 

5

 

E

 

F

A

 

B

C

D

 

6

 

F

 

A

B

 

C

D

E

The average production in a day is given as follows:

  

Operator

     
  

1

2

3

4

5

6

Time Period

1

142

148

149

149

154

147

 

2

145

150

152

155

148

151

 

3

149

147

151

148

148

150

 

4

138

141

146

145

149

147

 

5

141

153

152

151

151

149

 

6

147

149

150

146

150

148

Assuming that the effect of each operator, time-period and machine are normally distributed with approximately equal variances, analyse the design at \(1 \%\) level of significance. Test whether the effect of the different operators, time periods and machines on the production are significant or not. If significant, do the pair-wise comparison between them.

\(sin\left(2\theta \right)=2\:sin\:\theta \:cos\:\theta \)

MSTL-001 Sample Solution 2023

 

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\(c=a\:cos\:B+b\:cos\:A\)

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