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

Time	A	B	C	F	Row Total
1 h	24	43	61	10	138
Unlimited	16	45	83	18	162
Column Total	40	88	144	28	300

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


State the null and alternate hypotheses.

H₀: Time to take a test and test score arenot independent.
H₁: Time to take a test and test score areindependent. H₀: The distributions for a timedtest and an unlimited test are the same.
H₁: The distributions for a timed test and anunlimited test are different.    H₀: The distributions for a timed test and anunlimited test are different.
H₁: The distributions for a timed test and anunlimited test are the same. H₀: Time to take atest and test score are independent.
H₁: Time to take a test and test score are notindependent.

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


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

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

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

At the 1% level of significance, there is insufficient evidenceto claim that time to do a test and test results are notindependent. At the 1% level of significance, there is sufficientevidence to claim that time to do a test and test results are notindependent.