Question

Some people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 12 units were defective.

a. What is the sample porportion

b. Determine a 95% confidence interval for the percentage of defective systems.

c. If you want the margin of estimate error over the defective proportion to be within ± 0.5% margin of error (with the same confidence of 95%), how many units should be sampled?

Answer 1

Solution:

a)

n = 1200

x = 1

Point estimate = sample proportion = = x / n = .0.01

1 - = 1-0.01 = 0.99

Z/2 = 1.960

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

= 1.960* ((0.01*(0.99) / 1200)

= 0.0056

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.01-0.0056 < p < 0.01+0.0056

0.0043 < p < 0.0156

( 0.0043 , 0.0156 )

c)

= 0.01

1 - = 1-0.01 = 0.99

margin of error = E = 0.005

Z/2 = 1.96

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

= (1.96/0.005)2 *0.01*0.99

= 1521

sample size = n = 1521