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A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the results shown below. For example, the number "1" appeared on 40 rolls.
-What is the null hypothesis for this chi-square goodness of fit test?
A) The probabilities of a 1, 2, …, 6 are 40/180, 40/180, …, 20/180, respectively.
B) The die is not fair: the probabilities of getting a particular number (e.g. "1") are not all equal.
C) The die is fair: the probability of getting any particular number (e.g. "1") is 1/6.
D) None of the above

Question

Use the following information for questions:
 A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the results shown below. For example, the number "1" appeared on 40 rolls. 
-What is the null hypothesis for this chi-square goodness of fit test?
A) The probabilities of a 1, 2, …, 6 are 40/180, 40/180, …, 20/180, respectively. 
B) The die is not fair: the probabilities of getting a particular number (e.g. "1") are not all equal. 
C) The die is fair: the probability of getting any particular number (e.g. "1") is 1/6. 
D) None of the above

Quizplus · Accepted Answer

The null hypothesis for a chi-square goodness of fit test typically posits that there is no significant difference between the observed frequencies and the expected frequencies under a specific distribution. In the context of testing whether a die is fair, the null hypothesis would state that each outcome (rolling a 1, 2, 3, 4, 5, or 6) has an equal probability of 1/6, as this represents the expected distribution of outcomes for a fair die.

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