Question

A researcher wishes to know with 95% confidence the proportion of people who own a desktop computer. A previous study showed that 40% of those interviewed owned a desktop. The researcher wishes to be accurate within 2% of the true proportion.

Find the minimum sample size necessary.

Answer 1

SOLUTION:

From given data,

A researcher wishes to know with 95% confidence the proportion of people who own a desktop computer. A previous study showed that 40% of those interviewed owned a desktop. The researcher wishes to be accurate within 2% of the true proportion.

From the standard normal table,

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

$\alpha$ = 1 - Confidence interval = 1-0.95 = 0.05

$\alpha$/2 = 0.05 / 2

= 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

the z-critical value at 95% confidence is 1.96

The information represent

E = 2% = 2/100 = 0.02

$\hat{p}$ = 40% = 40/100 = 0.40

Find the minimum sample size

sample size = n = (Z_$\alpha$/2 / E)² * $\hat{p}$ (1-$\hat{p}$)

n = (1.96/ 0.02)² * 0.40(1-0.40)

n = 9604 *0.24

n = 2304.96

The minimum sample size is 2305

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