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Statistics and probability

Course: Statistics and probability > Unit 10

Lesson 2: Sampling distribution of a sample proportion

Mean and standard deviation of sample proportions

An organization is considering having a "Bring your pet to work" day. The administration takes an

of 35 of their employees and finds that 20, percent of those sampled are allergic to pets. Administration is considering taking more samples like this. Suppose that of all 500 employees of the organization, it's actually 10, percent that are allergic.

Let p, with, hat, on top represent the proportion of a sample of 35 employees that are allergic to pets.

What are the mean and standard deviation of the sampling distribution of p, with, hat, on top?

(Choice A)
$\begin{aligned} \mu_{\hat p}&=0.2 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.2(1-0.2)}{35}} \end{aligned}$
(Choice B)
$\begin{aligned} \mu_{\hat p}&=0.1 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.1\left(1-0.1\right)}{500}} \end{aligned}$
(Choice C)
$\begin{aligned} \mu_{\hat p}&=0.2 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.2(1-0.2)}{500}} \end{aligned}$
(Choice D)
$\begin{aligned} \mu_{\hat p}&=0.1 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.1\left(1-0.1\right)}{35}} \end{aligned}$

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Statistics and probability

Course: Statistics and probability > Unit 10

Problem