Question

Question

Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 84 times and record the outcomes in the table below.

Outcome	1	2	3	4	5	6
Expected	14	14	14	14	14	14
Observed	17	12	15	5	16	19

They perform a chi-square Goodness-of-Fit Test. The first few steps are summarized below.

• H0: The die is fair.
  Ha: The die is not fair.
• α=0.01
• The test statistic, χ20=8.857.

Use the following portion of the χ2-table for the critical value.

df	χ20.10	χ20.05	χ20.025	χ20.01	χ20.005
...	…	…	…	…	…
4	7.779	9.488	11.143	13.277	14.860
5	9.236	11.070	12.833	15.086	16.750
6	10.645	12.592	14.449	16.812	18.548
7	12.017	14.067	16.013	18.475	20.278
8	13.362	15.507	17.535	20.090	21.955

Which is the correct conclusion of our goodness-of-fit test, at the 1% significance level?

Select the correct answer below:

Degrees of freedom =5.

Critical value: χ20.01=16.750.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should reject H0 because the test statistic falls in the rejection region (less than χ20.01).

Degrees of freedom =5.

Critical value: χ20.01=15.086.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should reject H0 because the test statistic falls in the rejection region (less than χ20.01).

Degrees of freedom =6.

Critical value: χ20.01=18.548.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should reject H0 because the test statistic falls in the rejection region (less than χ20.01).

Degrees of freedom =5.

Critical value: χ20.01=15.086.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should not reject H0 because the test statistic does not fall in the rejection region (greater than χ20.01).

Degrees of freedom =6.

Critical value: χ20.01=16.812.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should not reject H0 because the test statistic does not fall in the rejection region (greater than χ20.01).

Degrees of freedom =5.

Critical value: χ20.01=16.750.

Conclusion: The test statistic is less than the critical value χ20<χ20.01. So, we should not reject H0 because the test statistic does not fall in the rejection region (greater than χ20.01).

Answer 1