Question

conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.
a person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. here are the observed frequencies for the outcomes
of 1, 2, 3, 4, 5, and 6, respectively: 26, 32, 50, 40, 28, 24. use a 0.10 significance level to test the claim that the outcomes are not equally likely. does it
appear that the loaded die behaves differently than a fair die?
click here to view the chi - square distribution table.
the test statistic is 15.260.
(round to three decimal places as needed.)

Explanation:

Step1: Determine Degrees of Freedom

For a die with 6 outcomes, degrees of freedom \( df = 6 - 1 = 5 \).

Step2: Find Critical Value

Using the chi - square distribution table, for \( df = 5 \) and significance level \( \alpha = 0.10 \), the critical value is found by looking at the row with \( df = 5 \) and the column with area to the right \( 0.10 \). From the table, the critical value is \( 9.236 \).

Step3: Compare Test Statistic and Critical Value

The test statistic is \( 15.260 \) and the critical value is \( 9.236 \). Since \( 15.260>9.236 \), we reject the null hypothesis (the claim that outcomes are equally likely). So, the loaded die behaves differently than a fair die.

Answer:

Test Statistic: \( 15.260 \), Critical Value: \( 9.236 \), Conclusion: Reject the null hypothesis, the loaded die behaves differently than a fair die.