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Answers without the blur. Sign up and see all textbooks for free! Q. 11

Expert-verified Found in: Page 800 ### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339 # A survey ﬁrm wants to ask a random sample of adults in Ohio if they support an increase in the state sales tax from $5%$% to $6%$, with the additional revenue going to education. Let $\stackrel{^}{p}$ denote the proportion in the sample who say that they support the increase. Suppose that $40%$ of all adults in Ohio support the increase. How large a sample would be needed to guarantee that the standard deviation of $\stackrel{^}{p}$ is no more than $0.01$?(a)$1500$(b) $2400$(c) $2401$(d) $2500$(e) $9220$

The sample that would be needed to guarantee that the standard deviation of $\stackrel{^}{p}$ is no more than$0.01$ is b) $2400$.

See the step by step solution

## Step 1: Given Information

We are given that the $\stackrel{^}{p}$denote the proportion in the sample who say that they support the increase.

We need to find that sample would be needed to guarantee that the standard deviation of $\stackrel{^}{p}$ is no more than $0.01$.

## Step 2: Simplify

First of all , we will use standard deviation for the estimation because it is proportion to population,

$SD$$\left(\stackrel{^}{p}\right)=\sqrt{\frac{p×\left(1-p\right)}{n}}$, here $\stackrel{^}{p}$ denote the proportion in the sample who say that they support the increase, we have to find out $n$.

Now standard deviation should not be more than $0.01$

$\sqrt{\frac{0.4×0.6}{n}}\le 0.01⇒\frac{0.4×0.6}{n}={0.01}^{2}$

We will multiply $n$ on other side, by simplifying we will find value of $n$;

$n\ge \frac{0.4×0.6}{{0.01}^{2}}⇒n\ge 2400$

If the sample size is at least $2400$ then condition would be satisfied which is standard deviation would be $0.01$ or less . So answer is $2400$. ### Want to see more solutions like these? 