Question

A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?.

Answer 1

Using the Central Limit Theorem, since there is less than 10 failures in the sample, it is not appropriate to assume that the sampling distribution of the sample proportion is approximately normal.

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$, as long as $np \geq 10$ and $n(1 - p) \geq 10$, that is, if there are at least 10 successes and 10 failures in the sample.

In this problem, 28 out of 30 people selected indicated that they rode the subway to work, that is, there are 28 successes and 2 failures in the sample.

Hence, since there is less than 10 failures in the sample, it is not appropriate to assume that the sampling distribution of the sample proportion is approximately normal.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/16695444