Question

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

Time	A	B	C	F	Row Total
1 h	24	42	66	11	143
Unlimited	18	47	85	7	157
Column Total	42	89	151	18	300

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

Answer 1

Result:

Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent.

Time	A	B	C	F	Row Total
1 h	24	42	66	11	143
Unlimited	18	47	85	7	157
Column Total	42	89	151	18	300

Ho: time to complete a test and test results are independent.

H1: time to complete a test and test results are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Time	A	B	C	F	Total		fo-fe
1 h	24	42	66	11	143		3.9800	-0.4233	-5.9767	2.4200
Unlimited	18	47	85	7	157		-3.9800	0.4233	5.9767	-2.4200
Total	42	89	151	18	300
Expected Frequencies
	Column variable
Time	A	B	C	F	Total		(fo-fe)^2/fe
1 h	20.0200	42.4233	71.9767	8.58	143		0.7912	0.0042	0.4963	0.6826
Unlimited	21.9800	46.5767	79.0233	9.42	157		0.7207	0.0038	0.4520	0.6217
Total	42	89	151	18	300
Data
Level of Significance	0.01
Number of Rows	2
Number of Columns	4
Degrees of Freedom	3
Results
Critical Value	11.3449
Chi-Square Test Statistic	3.7725
p-Value	0.2871
Do not reject the null hypothesis

test statistic = 3.77

(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

Since p value > 0.01 level of significance, Ho is not rejected.

We conclude that time to complete a test and test results are independent.