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	22	43	64	12	141
Unlimited	17	49	86	7	159
Column Total	39	92	150	19	300

Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-square for testing σ² or σ.

Chi-square test of independenceChi-square goodness of fit     Chi-square for testing σ² or σChi-square test of homogeneity

(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 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: 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: 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 > 0.1000.050 < 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 < α, we fail to reject the null hypothesis.Since the P-value ≥ α, we reject the null hypothesis.     Since the P-value is ≥ α, we fail to 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

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