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Chapter 3: Q.46 (page 192)
How much gas? Refer to Exercise . During March, the average temperature was 掳F and Joan used cubic feet of gas per day. Find and interpret the residual for this month.
The residual is and its negative; this shows the data point lies below the line.
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In its Fuel Economy Guide for model vehicles, the Environmental Protection Agency gives data on vehicles. There are a number of outliers, main vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other
or so vehicles are approximately Normal with a mean of miles per gallon (mpg) and a standard deviation of mpg.
The top How high must a vehicle鈥檚 gas mileage be in order to fall in the top of all vehicles? (The distribution omits a few high outliers, mainly hybrid gas-electric vehicles.)
Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:
(a) How would change if the bones had been measured in millimeters instead of centimeters? (There are millimeters in a centimeter.)
(b) If the and variables are reversed, how would the correlation change? Explain.
Merlins breeding The percent of an animal species in the wild that survives to breed again is often lower following a successful breeding season. A study of merlins (small falcons) in northern Sweden observed the number of breeding pairs in an isolated area and the percent of males (banded for identification) that returned the next breeding season. Here are data for nine years:
Investigate the relationship between breeding pairs and percent return. Follow the four-step process.
One of nature鈥檚 patterns connects the percentage of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for colonies of sparrow-hawks:
Make a scatterplot by hand that shows how the number of new adults relates to the percentage of returning birds.
Airlines have increasingly outsourced the maintenance of their planes to other companies. Critics say that the maintenance may be less carefully done so outsourcing creates a safety hazard. As evidence, they point to government data on the percent of major maintenance outsourced and the percent of flight delays blamed on the airline (often due to maintenance problems): Make a scatterplot by hand that shows how delays relate to outsourcing.
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