fair die 60 times, resulting in the distribution of dots shown. Research A stude

Question

fair die 60 times, resulting in the distribution of dots shown. Research A student rolled = .10, can you reject the hypothesis that the die is fair? a supposedly question: At Number of Dots 7Total 0.10 9.236 Back to Home 0 4934 10 4 0 167 5 0 167 6 0 167 10 10 0 90 0.00 10 57. If the null hypothesis holds true, what is the expected number of 1's to appear in the experiment? 58. If the decision rule is stated as: Reject Ho ifxtu what is the critical value for the test given a significance level of 0.10? s9. What is the p-value for the test? 0.4934 60. Based on the output above, which conclusion is correct? a. Reject HO and conclude that the die is not fair b. Fail to Reject HO and conclude that the die is not fair c. Reject HO and conclude that the die is fair d. Fail to Reject HO and conclude that the die is fair e. None of the above

Explanation / Answer

57.

The null hypothesis is that the die is fair.

So, the probability of getting 1 = 1/6

The die is rolled 60 times,

So, if the null hypothesis is true, the expected no. of 1's to appear = 60*1/6 = 10

58.

There are 6 groups of observations in this experiment.

=> k = 6

If the null hypothesis is true,

The test statistic follows a chi-square distribution with degrees of freedom = k-1 = 5

we reject the null hypothesis for large values of the test statistic.

At significance level of 0.10,

the critical value is = 9.236357

because:

> qchisq(0.9, 5)
[1] 9.236357

So, at significance level of 0.10, we reject the null hypothesis if the value of the test statistic is greater than 9.236357

59.

computed test statistic value = 4.4

p-value

= P(test statistic >= 4.4)

= 0.4934

because:

> 1 - pchisq(4.4, 5)
[1] 0.4933735

60.

Since the p-value is greater than the level of significance,

we fail to reject the null hypothesis and

conclude that the die is fair

Hence, the answer is - D

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