a student believes that a certain number cube is unfair and is more likely to land with a six facing up. the…
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?\n\nyes, the conditions for inference are met.\nno, the 10% condition is not met.\nno, the randomness condition is not met.\nno, the large counts condition is not met.
Answer
Answer:
D. No, the Large Counts Condition is not met.
Explanation:
Step1: Recall conditions for proportion inference
For constructing a confidence - interval for a proportion, we need randomness, 10% condition and large - counts condition.
Step2: Check randomness
The student rolls the number cube, which can be considered a random process. So randomness condition is likely met.
Step3: Check 10% condition
We assume the number of all possible rolls of the cube is much larger than the sample of 15 rolls. So 10% condition is likely met.
Step4: Check large - counts condition
The large - counts condition for a proportion is $np\geq10$ and $n(1 - p)\geq10$. Here, $n = 15$ and $\hat{p}=\frac{5}{15}=\frac{1}{3}$. Then $n\hat{p}=15\times\frac{1}{3}=5<10$ and $n(1-\hat{p})=15\times(1 - \frac{1}{3})=10$. Since $n\hat{p}<10$, the large - counts condition is not met.