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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.

H_{0}: Extra time is independent of grade

Ha: Grade is dependent on extra time given.

1 hour | Unlimited time | |
---|---|---|

A | 41 | 59 |

B | 60 | 76 |

C or less | 70 | 59 |

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.

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.