Question

You wish to estimate, with 95% confidence (z*=1.96), the proportion of computers that need repairs or have problems by the time the product is 3 years old. Your estimate must be accurate within 3% of the true proportion. Find the minimum sample size needed, using a prior study that found that 19% of computers needed repairs or had problems by the time the product was three years old. Round your answer to the appropriate integer.

Answer 1

Solution :

Given that,

= 19%=0.19

1 - = 1 - 0.19 = 0.81

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.03)2 * 0.19 * 0.81

= 656.9

Sample size =657