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A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls the number cube 15 times and finds that the cube lands with a six facing up five times. The student wants to construct a 99% confidence interval for the proportion of times this number cube lands with a six facing up. Are the conditions for inference met?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the randomness condition is not met.
D. No, the Large Counts Condition is not met.

Answer :

Based on the given confidence interval, the correct option is D. No, the Large Counts Condition is not met.

Confidence Interval:

Basically, this is an operation which is used to measure probability that a parameter will fall between a pair of values around the mean are called as confidence interval.

Given,

A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls the number cube 15 times, and finds that the cube lands with a six facing up five times. The student wants to construct a 99% confidence interval for the proportion of times this number cube lands with a six facing up.

Here we need to find the conditions of inference are met or not.

Based on the the 99% confidence interval for the true proportion of times the number cube would land with a six facing up is 0.27 ± 2.58.

Because, 99 % confidence level is closer to 2.58 and 12 times facing up out of 45 times which is 12/45= .27

Therefore, the reason why option D No, the Large Counts Condition is not met.

To know more about Confidence interval here.

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