A die is rolled 180 times and the following data are obtained. Number Frequency
1 31
2 34
3 26
4 16
5 32
6 41
A chi-square test was conducted to determine whether or not the die is loaded (i.e.,that the six numbers are not equally likely) .Use a 5% level of significance. $x ^ { 2 }$ = 11.8; P-value = 0.03763

A) Reject the null hypothesis.The data provide sufficient evidence to conclude that the die is loaded.
B) Reject the null hypothesis.The data provide sufficient evidence to conclude that the die is fair.
C) Do not reject the null hypothesis.The data provide sufficient evidence to conclude that the die is loaded.
D) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded.
E) Reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded.

Question

A die is rolled 180 times and the following data are obtained. Number Frequency
1 31
2 34
3 26
4 16
5 32
6 41
A chi-square test was conducted to determine whether or not the die is loaded (i.e.,that the six numbers are not equally likely) .Use a 5% level of significance.

x ^ { 2 }

= 11.8; P-value = 0.03763

A) Reject the null hypothesis.The data provide sufficient evidence to conclude that the die is loaded.
B) Reject the null hypothesis.The data provide sufficient evidence to conclude that the die is fair.
C) Do not reject the null hypothesis.The data provide sufficient evidence to conclude that the die is loaded.
D) Do not reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded.
E) Reject the null hypothesis.The data do not provide sufficient evidence to conclude that the die is loaded.

Luciano Bossa · Accepted Answer

Final Answer : A, Explanation :  The null hypothesis is that the die is fair (i.e., the six numbers are equally likely). The alternative hypothesis is that the die is loaded (i.e., the six numbers are not equally likely). The chi-square test statistic is 11.8, and the corresponding p-value is 0.03763. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. Therefore, the data provide sufficient evidence to conclude that the die is loaded.

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