Question

In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?

Answer 1

Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.

What does the Central Limit Theorem state?

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$.

In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213

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