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	25	41	61	11	138
Unlimited	16	44	83	19	162
Column Total	41	85	144	30	300

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: The distributions for a timed test and an unlimited test are the same.
H₁: The distributions for a timed test and an unlimited test are different.

H₀: The distributions for a timed test and an unlimited test are different.
H₁: The distributions for a timed test and an unlimited test are the same.   

H₀: Time to take a test and test score are independent.
H₁: Time to take a test and test score are not independent.

H₀: Time to take a test and test score are not independent.
H₁: Time to take a test and test score are independent.

(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 > 0.100

0.050 < P-value < 0.100

   0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(iv) Conclude the test.

Since the P-value ≥ α, we reject the null hypothesis.Since the P-value < α, we do not reject the null hypothesis.    

Since the P-value is ≥ α, we do not reject the null hypothesis.Since the P-value < α, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent.

At the 1% level of significance, there is sufficient evidence to claim that time to do a test and test results are not independent.  

Answer 1

i) value of the level of significance =0.01

H₀: Time to take a test and test score are independent.
H₁: Time to take a test and test score are not independent.

ii)

Applying chi square test:

Expected	Ei=row total*column total/grand total	A	B	C	F	Total
	1 h	18.86	39.10	66.24	13.80	138
	Unlimited	22.14	45.90	77.76	16.20	162
	total	41	85	144	30	300
chi square    χ2	=(Oi-Ei)2/Ei	A	B	C	F	Total
	1 h	1.999	0.092	0.415	0.568	3.074
	Unlimited	1.703	0.079	0.353	0.484	2.618
	total	3.702	0.171	0.768	1.052	5.6924

sample test statistic =5.69

iii)

P-value > 0.100

iv) Since the P-value is ≥ α, we do not reject the null hypothesis

v)

At the 1% level of significance, there is insufficient evidence to claim that time to do a test and test results are not independent.