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-valueExplanation / 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
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