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You want to estimate the proportion of students at OSU who have ever used an online dating app. You select a random sample of 140 OSU students and find that 43% have used an online dating app. If you want to construct a 99% confidence interval, what will the margin of error be? Try not to do a lot of rounding along the way until you get to the end of your calculations?

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Answer:

The margin of error for the proportion of students at OSU who have ever used an online dating app in 99% confidence level is 10.8%

Step-by-step explanation:

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

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

  • z is the corresponding statistic in the given confidence level (2.58)
  • p  the proportion of students at OSU who have ever used an online dating app in the random sample. (0.43)
  • N is the sample size (140)

Putting the numbers in the formula we get

ME=[tex]2.58*\sqrt{\frac{0.43*0.57}{140} }[/tex] ≈ 0,10795 ≈ 10.8%

Then the confidence interval for the proportion of students at OSU who have ever used an online dating app in 99% confidence level would be 43%±10.8%

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