Question

a and b please

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 4 percentage points with 95% confidence if (a) he uses a previous estimate of 28%? (b) he does not use any prior estimates? Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) n = (Round up to the nearest integer.) (b)n- (Round up to the nearest integer.)

Answer 1

C- level = 95% =0.95

a = 1-0.95 = 0.05

$\frac{\alpha}{2} =\frac{0.05}{2}=0.025$

Area =1--=1 – 0.025 = 0.975

Using Z table check 0.975 in the middle of the table and note correspoding row and column number to get critical value or use excel command =NORMSINV(0.975)

Zc = critical value = 1.96

E = 0.04

Part a :

p = 28% = 0.28

Sample size :

$n = p*(1-p)*\left ( \frac{Zc}{E} \right )^2$

$n = 0.28*(1-0.28)*\left ( \frac{1.96}{0.04} \right )^2$

$n = 0.2016*\left ( 49 \right )^2$

n = 0.2016 *2401

n = 484 . 0416

Answer : n = 484                  ( rounded )

Part b .

Not any prior estimate is given

p = 0.50

Sample size :

$n = p*(1-p)*\left ( \frac{Zc}{E} \right )^2$

$n = 0.50*(1-0.50)*\left ( \frac{1.96}{0.04} \right )^2$

$n = 0.25*\left ( 49 \right )^2$

n = 0.25 *2401

n = 600.25

Answer : n = 600