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12. -6 points 10.R.006 Professor Far believes that extra tine does not i prove g

ID: 3368597 • Letter: 1

Question

12. -6 points 10.R.006 Professor Far believes that extra tine does not i prove grades on exems. H¢ ra d mly ?? ded a group of 300 students into two groups @nd gave them all the same test. One group had exactly 1 hour in long os desired. The results ar showm in the following table. Test at the 0.01 level of significance that time to complete @ test and test results are independent. hich to finish the test and t e other group could stay as Column Total (Give the valuc of the level of significance State the null and alternate hypotheses Ho: Tests A, B, C, F are independent Ho: The distributions for timed test and an unlimited test @?the same. Ho: Time to take a test and test score are independent. Ho: Timed tests and unlimited time to take a test are independent. H1: Tests A, B, C, Fare not indepandent. M1: The distributions for a timed test and an unlimited test are different. H1: Time to take a test and test score are not independent. H1: Timed tests and unlimited t me to take test are not independent. () Find the sample test statistie. (Round your answer to two decimal places.) (iii) Find or estimate the A-value of the sample test statistic. [Round your answer to three decimal places.) (iv) Conclude the test Since P-value

Explanation / Answer

Solution

i) H0: Time to do a test and the test scores are independent.

   H1: Time to do a test and the test scores are not independent.

Third option ANSWER 1

ii) Test statistic: ?2 = 8.91 ANSWER 2

iii) p-value = 0.031 ANSWER 3

iv) Conclusion: Since p-value ? ?, we do not reject the null hypothesis.

Second Option ANSWER 4

v) Interpretation: At 1% level of significance, there is insufficient evidence to claim that Time to do a test and the test scores are not independent. First Option ANSWER 5

Details of Calculations

CONTINGENCY

(2 x 4)

r =

2

c =

4

DF =

3

       Chi-square Cal =

8.910633731

       Chi-square Crit =

11.34486668

for

? =

0.01

p-value =

0.030502961

Oij

A

B

C

D

Total Oi.

1 hr test

24

45

56

10

135

Unlimited

15

45

83

22

165

Total O.j

39

90

139

32

300

Eij = (Oi. xO.j)/N

A

B

C

D

Total

1 hr test

17.55

40.5

62.55

14.4

135

Unlimited

21.45

49.5

76.45

17.6

165

Total

39

90

139

32

300

CHECK: respective row totals, column totals and grand total of

both Oij and Eij must be equal

(Oij - Eij)^2/Eij

A

B

C

D

Total

1 hr test

2.370513

0.5

0.685891

1.34444

4.900849

Unlimited

1.93951

0.409090909

0.561184

1.1

4.009785

Total

4.310023

0.909090909

1.247075

2.44444

8.910634

DONE

CONTINGENCY

(2 x 4)

r =

2

c =

4

DF =

3

       Chi-square Cal =

8.910633731

       Chi-square Crit =

11.34486668

for

? =

0.01

p-value =

0.030502961