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 hourin 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 24 43 64 12 143 Unlimited 16 47 84 10 157 Column Total 40 90 148 22 300Classify 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 homogeneityChi-square test of independence Chi-square for testing σ2 or σChi-square goodness of fit (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: Time to take a test and test score are not independent. H1: Time to take a test and test score are independent. 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 different. H1: The distributions for a timed test and an unlimited test are the same. (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.

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 hourin 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	24	43	64	12	143
Unlimited	16	47	84	10	157
Column Total	40	90	148	22	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 homogeneityChi-square test of independence Chi-square for testing σ² or σChi-square goodness of fit

(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: Time to take a test and test score are not independent.
H₁: Time to take a test and test score are independent. 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 different.
H₁: The distributions for a timed test and an unlimited test are the same.

(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.