Question

Many people who bought Z-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective. Determine the upper limit for the 95% confidence interval for the population proportion. Round your answer to three decimals.

Answer 1

The upper limit for the 95% confidence interval for the population proportion of defective gaming systems is 0.022

Explanation:

Upper Limit for 95% Confidence Interval can be calculated using p+ME where

• p is the sample proportion of defective gaming systems (
  `(18)/(1200) = 0.015`)

• ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=
`(z*√(p*(1-p)))/(√(N) )` where

• z is the statistic of 95% confidence level (1.96)

• p is the sample proportion (
  `(18)/(1200)=0.015`

• N is the sample size (1200)

Using the numbers we get:

ME=
`(1.96*√(0.015*0.985))/(√(1200) )` ≈ 0.007

Then upper limit for the population proportion is 0.015+0.007 =0.022