# (Solved): A professor believes that extra time does not improve grades on exams. He randomly divided a group o ...

A professor believes that extra time does not improve grades on exams. He randomly divided a group of 365 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 the claim that the time to complete a test and test results are independent at the 0.02 significance level.

H0: Extra time is independent of grade
Ha: Grade is dependent on extra time given.

1 hourUnlimited time
A 4159
B6076
C or less7059

a. Complete the table: Give all answers as decimals rounded to 4 places.

Observed
Frequency
Expected
Frequency
(O−E)2E(�-�)2�
41
59
60
76
70
59
Total

(b) What is the chi-square test-statistic for this data?
Test Statistic: χ2=�2=

(d) The p-value is...

• greater than α�
• less than (or equal to) α�

(e) The p-value leads to a decision to...

• reject the null hypothesis
• fail to reject the null hypothesis

(f) What is the final conclusion?

• There is not sufficient evidence to conclude grade is dependent on extra time.
• There is sufficient evidence to conclude grade is dependent on extra time.

We have an Answer from Expert

Solution:- Given

Null and Alternative Hypothesis:
Extra time is independent of grade.
Grade is independent on extra time given.
Expected value
Row total.
Column total
Grand total
Squared distances =

In this step, we formulated the hypothesis and provided the formulas.

We have an Answer from Expert