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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10Develop a 95% confidence interval estimating of the population mean rating for Miami. Round your answers to two decimal places. Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your numerical answer (i.e. use 1200 instead of 1,200, etc.)

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Answer:

Confidence Interval in 95% confidence level for the quality rating is (6.06,7.46)

Step-by-step explanation:

Confidence Interval can be calculated using the formula M±ME where

  • M is the mean of the sample
  • ME is the margin of error in a given confidence level

Using the sample obtained from 50 business travelers we get

  • Mean of the sample is 6.76
  • standard deviation of the sample is 2.526

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 95% confidence level (1.96)
  • s is the standard deviation of the sample (2.526)
  • N is the sample size (50)

Using the numbers in the formula we get:

ME=[tex]\frac{1.96*2.526}{\sqrt{50} }[/tex] ≈ 0.70

Then the confidence interval becomes 6.76±0.70

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