Question

A random sample of 75 printers discovered that 15 of them were being used in small businesses . find the 90% limit for the population proportion of printers that are used in small businesses.

Answer 1

Sample = 75 printers, Printers used by small businesses = 15

p(15) = 15/75 = 0.2

At 90% limit, Z =1.64

Limit of proportion of printers used by small business = p +/- Z Sqrt [p(1-p)/n]

=0.2 +/- 1.64 * Sqrt [0.2(1-0.2)/75] = 0.2 +/- 0.0757

Limit of proportion => (0.2-0.0757) to (0.2+0.0757) => 0.1243 to 0.2757 or 12.43% to 27.57%