For Problems 5-14, 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)-(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.
Fair Dice: Uniform Distribution. 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:
Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
Observed frequency 0 | 62 | 45 | 43 | 32 | 47 | 51 |
Do these data indicate that the die is unbalanced? Use a 1% level of significance.
Hint: If the die is balanced, all outcomes should have the same expected frequency.
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Chapter 11 Solutions
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