For Problems 5–16, please provide the following information.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population ­fits the speci­fied distribution of categories?

(e) Interpret your conclusion in the context of the application.

A gambler complained about the dice. They seemed to be loaded! The dice were taken off the table and tested one at a time. One die was rolled 300 times and the following frequencies were recorded.

Dot these data indicate that the die is unbalanced? Use a 1% level of significance.

If the die is balanced, all outcomes should have the same expected frequency.

Outcome 1 234 5 6 Observed frequency O 62 45 63 32 47 51