Question

Q2: 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?.

*Do not generate the table by using Excel

Time	A	B	C	F	Total
1 hour	20	45	61	14	140
Unlimited	19	44	83	14	160
Total	39	89	144	28	300

Answer 1

The hypothesis being tested is:

H₀: Time to complete the test and the result is independent

H_a: Time to complete the test and result is not independent

The calculations are:

1 hour	20	45	61	14	140
Unlimited	19	44	83	14	160
Total	39	89	144	28	300
Expected values	A	B	C	F	Total
1 hour	18.2	41.53333	67.2	13.06667	140
Unlimited	20.8	47.46667	76.8	14.93333	160
Total	39	89	144	28	300
O-E	A	B	C	F	Total
1 hour	1.8	3.466667	-6.2	0.933333	0
Unlimited	-1.8	-3.46667	6.2	-0.93333	0
Total	0	0	0	0	0
(O-E)²/E	A	B	C	F	Total
1 hour	0.178022	0.289353	0.572024	0.066667	1.106065
Unlimited	0.155769	0.253184	0.500521	0.058333	0.967807
Total	0.333791	0.542536	1.072545	0.125	2.073872

Expected value = (Row Total*Colum Total)/Marginal Total

The chi-square test statistic is 2.07.

Df = (r - 1)*(c-1) = (4 - 1)*(2*1) = 3

The p-value from the chi-square table is 0.5572.

Since the p-value (0.5572) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Therefore, we cannot conclude that time to complete the test and the result is independent.