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	RowTotal
1 h	20	44	56	11	131
Unlimited	18	45	84	22	169
ColumnTotal	38	89	140	33	300

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


State the null and alternate hypotheses.

H₀: The distributions for a timed test andan unlimited test are different.
H₁: The distributions for a timed test and anunlimited test are the same.H₀: Thedistributions for a timed test and an unlimited test are thesame.
H₁: The distributions for a timed test and anunlimited test aredifferent.    H₀: Time totake a test and test score are not independent.
H₁: Time to take a test and test score areindependent.H₀: Time to take a test and testscore 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 > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < ?, we do not reject thenull hypothesis.Since the P-value < ?, wereject the null hypothesis.    Since theP-value is ? ?, we do not reject the nullhypothesis.Since the P-value ? ?, 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.