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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.

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Answer:

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

Step-by-step explanation:

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

  • p is the sample proportion of defective gaming systems ([tex]\frac{18}{1200} = 0.015[/tex])
  • ME is the margin of error from the mean

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

ME=[tex]\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }[/tex] where

  • z is the statistic of 95% confidence level (1.96)
  • p is the sample proportion ([tex]\frac{18}{1200}=0.015[/tex]
  • N is the sample size (1200)

Using the numbers we get:

ME=[tex]\frac{1.96*\sqrt{0.015*0.985}}{\sqrt{1200} }[/tex] ≈ 0.007

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

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