Question

The seller of a loaded die claims that it will favor the outcome 6.

Probability
ANSWERED
asked 2021-08-22
The seller of a loaded die claims that it will favor the outcome 6. We don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.
a) There's a 3% chance that the die is fair.
b) There's a 97% chance that the die is fair.
c) There 's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.
d) There's a 3% chance that a fair die could randomly produce the results we observed, so it's reasonable to conclude that the die is loaded.

Expert Answers (1)

2021-08-23

Given:
P=0.03=3%
Given claim : Die favors 6(when no favoring, we have 1 chance in 6 to roll a 6)
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.
\(\displaystyle{H}_{{0}}:{p}={\frac{{{1}}}{{{6}}}}\)
\(\displaystyle{H}_{{a}}:{p}{>}{\frac{{{1}}}{{{6}}}}\)
The P-value is the probability of obtaining the value of the test statistic, or a value more extreme, when the null hypothesis is true.
In this case, the P-value then means : there is a chance 3% of obtaining a sample proportion higher than \(\displaystyle\frac{1}{{6}}\), when the die is not loaded or fair.
Result: (c) is correct 

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