Question

To obtain an estimate of the failure rates, p, of a type of cellphones after exposure to water, 120 cellphones were sent for testing. After being dropped in water, 20 of them failed. Using the estimate for p from the study above, what sample size is needed so that the width of 98% confidence interval for p is 0.1 for future studies?

Answer 1

Solution :

Given that,

n = 120

x = 20

Point estimate = sample proportion = = x / n = 0.167

1 - = 0.833

margin of error = E = width / 2 = 0.05

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z/2 = Z0.01 = 2.326

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

= (2.326 / 0.05)2 * 0.167 * 0.833

= 301.05

sample size = 302