Professor Fair believes that extra time does not improve gra

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. Give the value of the level of significance. State the null and alternate hypotheses. Find the sample test statistic. (Round your answer to two decimal places.) Find or estimate the P-value of the sample test statistic (Round your answer to three decimal places ) Conclude test. Interpret the conclusion In the context of the application.

Solution

i)

alpha = 0.01 [GIVEN]

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OPTION C: Ho: Time to take atest and test score are independent.

H1: Time to take atest and test score are not independent.

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ii)

Doing an Expected Value Chart,          
          
18.5   46   56   14.5
18.5   46   56   14.5
sing chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    1.854514828   [ANSWER, TEST STATISTIC]

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III)  
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    4      
b =    2      
          
df =    3      
          
          
Also, the p value is, at alpha = 0.01,          
          
P =    0.60314435   [ANSWER]  

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iv)

OPTION B: As P >= alpha, we DO NOT REJECT HO.

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V)

OPTION A: There is INSUFFICIENT EVIDENCE...
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the variables are dependent to each other.