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Environmental engineers are using data collected by weather data centers to learn how climate affects the see ice. Of 536 ice melt ponds studied in a certain region, 97 were classified as having "firs-year ice". The researchers estimated that about 18% of melt ponds in the region hve firsl-year ice. Estimate, with 90% confidence, the percentage of all ice-melt ponds in the region that have first-year ince. Give a practical intepretation of the results. 

Construct a 90% confidence interval around the sample proportion of ice melt ponds with first-year ice. 

Interpret the confidence interval practically. Choose the correct answer below. 

  • . One can be 90% confident the tru proportion of ice melt ponds in the region with first-yea ice lies at the mean of the above interval, rather than 18%.
  • . Since 18% is not in the interval, one can be 90% confident the true proportion of ice melts ponds in the region with first-year ice is not 18%.
  • . One can be 90% confident the tru proportion of ice melt ponds in the region with first-year ice is within the above interval, and there is 90% chance it is 18%. 
  • . Since 18% is in the interval, one can be 90% confident the true porportion of ice melt ponds in the region with first-year ice is 18%. 
  • One can be 90% confidence the true porportion of ice melt ponds in the region with first-year ice is within the above interval, though it is probably not 18%. 

 

p^ = .18

90% confidence = Z.05 =1.645

.18 +/- 1.645 * sqrt((.18*.82)/536) =

(.1527 , .2073)

 

One can be​ 90% confident the true proportion of ice melt ponds in the region with​ first-year ice is within the above​ interval, though it is probably not 18​%.

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