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Born outside the United States Stu ID Age Total Crd Hrs GPA Hrs spend on sch...

Born outside the United States

Stu ID

Age

Total Crd Hrs

GPA

Hrs spend on sch wrk

205

26

48

2.90

25

209

57

23

2.98

7

198

32

78

3.40

8

230

44

34

3.70

10

135

19

0

3.00

4

178

34

51

3.50

8

224

23

26

3.00

20

328

45

23

3.25

12

169

19

23

3.00

4

164

26

51

3.8

2

266

49

20

3.91

10

202

20

12

3.60

4

219

57

35

2.98

7

167

37

56

2.86

3

324

21

24

3.80

8

179

16

15

3.90

12

45

19

44

2.80

10

32

24

44

3.70

4

246

34

60

2.90

4

174

19

23

3.30

12

303

21

51

2.00

2

242

19

50

3.40

10

184

25

35

3.10

5

272

19

31

3.4

12

9

18

12

4.00

25

228

21

18

3.50

5

226

24

12

2.43

6

146

26

0

3.20

10

318

20

13

2.70

4

44

25

50

3.00

4
  1. Using your sample of 30 foreign-born students, conduct a correlation test at the .05 level of significance to determine if there’s a statistically significant relationship between students GPA and the number of hours spent on homework. Give the value of the correlation coefficient r, the critical value of r, and your interpretation of the correlation coefficient r.
  2. Using your sample of 30 foreign-born students, conduct a correlation test at the .05 level of significance to determine if there’s a statistically significant relationship between students Age and the number of hours spent on homework. Give the value of the correlation coefficient r, the critical value of r, and your interpretation of the correlation coefficient r.
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Answer #1

For students GPA and the number of hours spent on homework:

Ʃx = 97.01
Ʃy = 257
Ʃxy = 851.48
Ʃx² = 319.9959
Ʃy² = 3231
Sample size, n = 30
SSxx = Ʃx² - (Ʃx)²/n = 319.9959 - (97.01)²/30 = 6.29789667
SSyy = Ʃy² - (Ʃy)²/n = 3231 - (257)²/30 = 1029.36667
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 851.48 - (97.01)(257)/30 = 20.4276667

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 20.42767/√(6.2979*1029.36667) = 0.2537

df = n-2 = 28

Critical value of r at 0.05, rc = 0.361

As |r| < rc, we fail to reject the null hypothesis.

There is no correlation between students GPA and the number of hours spent on homework.

-------------

For students Age and the number of hours spent on homework:

Ʃx = 839
Ʃy = 257
Ʃxy = 7035
Ʃx² = 27393
Ʃy² = 3231
Sample size, n = 30
SSxx = Ʃx² - (Ʃx)²/n = 27393 - (839)²/30 = 3928.96667
SSyy = Ʃy² - (Ʃy)²/n = 3231 - (257)²/30 = 1029.36667
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 7035 - (839)(257)/30 = -152.43333

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -152.43333/√(3928.96667*1029.36667) = -0.0758

df = n-2 = 28

Critical value of r at 0.05, rc = 0.361

As |r| < rc, we fail to reject the null hypothesis.

There is no correlation between students Age and the number of hours spent on homework.

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