The seller of a loaded die claims that it will favour the outcome 6.We don't believe that claim,and roll the die 350 times to test an appropriate hypothesis.Our P-value turns out to be 0.01.Provide an appropriate conclusion using α = 0.05.

A) We can say there is a 1% chance of not seeing a fair die in the results we observed from natural sampling variation.We conclude the die is loaded.
B) If the die does not favour the outcome 6,then there is only a 1% chance of seeing a sample proportion of the outcome 6 as high (or higher) than that which we observed from natural sampling variation.At α = 0.05,we reject the null hypothesis and conclude that the die will favour the outcome 6.
C) If the die does not favour the outcome 6,then there is only a 1% chance of seeing a sample proportion of the outcome 6 as high (or higher) than that which we observed from natural sampling variation.At α = 0.05,we fail to reject the null hypothesis that the die does not favour the outcome 6.That is,there is insufficient evidence to conclude that the die will favour the outcome 6.
D) There is a 1% chance of a fair die.
E) There is a 99% chance of a fair die.

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Kaitlyn McArthur · Accepted Answer

Final Answer : B, Explanation :  The P-value of 0.01 indicates that there is only a 1% chance of observing a sample proportion of 6s as high or higher than what was observed if the die were fair. Since this P-value is less than the significance level α = 0.05, we reject the null hypothesis, suggesting the die is indeed loaded in favor of 6.

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