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Chapter 3: Q. 2.5 (page 149)

In the chapter-opening Case Study (page 141), the Starnes family arrived at Old Faithful after it had erupted. They wondered how long it would be until the next eruption. Here is a scatterplot that plots the interval between consecutive eruptions of Old Faithful against the duration of the previous eruption, for the month prior to their visit.

What information does the Starnes family need to predict when the next eruption will occur?

Short Answer

Expert verified

The family wants to know how long it has been since the last eruption.

Step by step solution

01

Given Information

The scatter plot is:

02

Explanation

The Starnes family needed to know the length of the last eruption's period in order to anticipate the next one. It will aid in determining the duration and timing of the next eruption.

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Most popular questions from this chapter

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) Make a scatterplot. Do you think that all five specimens come from the same species? Explain.

(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for r. Explain how your value for rmatches your graph in (a).

The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 regions in Great Britain was re- corded. A scatterplot of spending on alcohol versus spending on tobacco is shown below. Which of the following statements is true?

(a) The observation (4.5,6.0) is an outlier.

(b) There is clear evidence of a negative association between spending on alcohol and tobacco.

(c) The equation of the least-squares line for this plot would be approximately y铃�=10鈭�2x

(d) The correlation for these data is r=0.99

(e) The observation in the lower-right corner of the plot is influential for the least-squares line.

A government report looked at the amount borrowed for college by students who graduated in 2000and had taken out student loans.12 The mean amount was x=\(17,776and the standard deviation was sx=\)12,034. The median was\(15,532and the quartiles were Q1=\)9900and Q3=\(22,500.

(a) Compare the mean and the median. Also compare the distances of Q1 and Q3 from the median. Explain why both comparisons suggest that the distribution is right-skewed.

(b) The right-skew pulls the standard deviation up. So a Normal distribution with the same mean and standard deviation would have a third quartile larger than the actual Q3.Find the third quartile of the Normal distribution with渭=\)17,776and 蟽=\(12,034and compare it withQ3=\)22,500.

To determine the least-squares regression line:

We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198vehicles in the government's 2008Fuel Economy Guide give the regression line predicted highway mpg=4.62+1.109(city mpg).

(a) What鈥檚 the slope of this line? Interpret this value in context.

(b) What鈥檚 the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted highway mileage for a car that gets 16miles per gallon in the city. Do the same for a car with a city mileage of 28mpg.

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