Question

Suppose the true proportion of voters in the county who support a restaurant tax is 0.54. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?

Answer 1

Answer:

The correct answer is:

(a) 0.54

(b) 0.0385

Step-by-step explanation:

Given:

Restaurant tax,

p = 0.54

Sample size,

n = 168

Now,

(a)

The mean will be:

⇒ μ $\hat{p}= p$

         $=0.54$

(b)

The standard error will be:

$\sigma \hat{p}$ = $\sqrt{[\frac{p(1-p)}{n} ]}$

    = $\sqrt{[\frac{(0.54\times 0.46)}{168} ]}$

    = $\sqrt{[\frac{(0.2484)}{168} ]}$

    = $0.0385$