Question

a six - sided die is rolled 120 times. fill in the expected frequency column. then, conduct a hypothesis test to determine if the die is fair. the data in table 11.34 are the result of the 120 rolls.state chi - square critical value. use alpha criterion of 0.05 (with two - tailed test) and chi - square table from your textbook - https://openstax.org/books/introductory - statistics - 2e/pages/h - tablesa. 12.833b. 14.449c. 11.070d. 20.515

Explanation:

Step1: Determine degrees of freedom

For a chi - square goodness - of - fit test with \(k\) categories, the degrees of freedom is \(df=k - 1\). Here, \(k = 6\) (number of faces of the die), so \(df=6 - 1=5\).

Step2: Find critical value

Using a two - tailed test with \(\alpha = 0.05\) and \(df = 5\), looking at the chi - square distribution table. The critical value for \(\chi^{2}\) with \(df=5\) and \(\alpha = 0.05\) (two - tailed) is \(11.070\).

Answer:

C. 11.070