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A researcher (Jack) comes to you and is interested in the average length of time a computer fan will run before it needs to be cleaned. Jack believes that this time period is approximately normally distributed with a standard deviation of 30 hours. You tell him to take a sample of computer fans. Jack comes back to you and says that he took a random sample of 36 computers, and found that the average length of time was 876 hours. Use a 94% confidence interval.

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Answer:

94% confidence interval for the average length of time a computer fan will run before it needs to be cleaned is between 866.6  and 885.4 hours

Step-by-step explanation:

94% confidence interval can be calculated using M±ME where

  • M is the sample average length of time before it needs to be cleaned. (876 hours)
  • ME is the margin of error from the mean

margin of error (ME) around the mean using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

  • z is the corresponding statistic in the 94%  confidence level (1.88)
  • s is the standard deviation of the time periods before it needs to be cleaned (30 hours)
  • N is the sample size (36)

Using the numbers we get ME=[tex]\frac{1.88*30}{\sqrt{36} }[/tex] =9.4

Then the 94% confidence interval is 876±9.4