Question

A random sample of 65 printers discovered that 31% of them were being used in small businesses. Find the 95% confidence interval for the population proportion of printers that are used in small businesses.

Answer 1

Solution :

n =65

= 0.310

1 - = 1 - 0.310 = 0.690

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.960 * (((0.310 * 0.690) / 65)

= 0.112

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.310 - 0.112 < p < 0.310 + 0.112

0.198 < p < 0.422