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	23	45	56	11	135
Unlimited	19	45	81	20	165
Column Total	42	90	137	31	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: 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.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 reject the null hypothesis.Since the P-value < α, we reject the null hypothesis.    Since the P-value is ≥ α, we do not reject the null hypothesis.Since the P-value < α, we do not 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) The 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) Sample test statistic = 4.60

(iii) P-value > 0.1000 (exact P-value = 0.2034

(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.

All calculations are done by statistical software R-STUDIO.