Question

Interpreting a Computer Display. In Exercises 9–12, refer to the display obtained by using the paired data consisting of Florida registered boats (tens of thousands) and numbers of manatee deaths from encounters with boats in Florida for different recent years (from Data Set 10 in Appendix B). Along with the paired boat, manatee sample data, StatCrunch was also given the value of 85 (tens of thousands) boats to be used for predicting manatee fatalities.

Finding a Prediction Interval For a year with 850,000 (x = 852) registered boats in Florida, identify the 95% prediction interval estimate of the number of manatee fatalities resulting from encounters with boats. Write a statement interpreting that interval.

Short answer

The 95% prediction interval of the number of manatee fatalities when there are 850,000 registered boats is equal to (50.033706, 90.929839).

This explains that for 850,000 registered boats, there is 95% confidence that the predicted number of manatee fatalities will fall between 50.03 and 90.93.

Step-by-step solution

Given information

Results are obtained for the linear relation between the variables “number of registered boats” and “number of manatee deaths” using StatCrunch.

Step 2:Prediction interval

It can be observed in the results table that for 850,000 registered boats 850,000, the 95% prediction interval for the number of manatee fatalities resulting from encounters with boats is obtained as (50.033706,90.929839).

This can be interpreted in the form that when the value of X (registered boats) is 850,000, there is 95% confidence that the predicted value of the number of manatee fatalities will lie between 50.03 and 90.93.