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Chapter 12: Q. 48 (page 792)

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance=490(time)2. A scatterplot of the students鈥� data showed a clear curved pattern. A scatterplot of which of the following should have a roughly linear pattern?

(a) [time, ln(distance)]

(b) [ln(time), distance]

(c) [ln(time), ln(distance)]

(d) [ln(distance), time]

(e) [distance, ln(time)]

Short Answer

Expert verified

A scatterplot that has a roughly linear pattern is option (c) [ln(time), ln(distance)] .

Step by step solution

01

Given information

Given in the question that, the theoretical relationship between the variables is the distance =490(time)2.

02

Explanation

According to the result of exercise 47,

The transformationsdistanceand time2are are single transformations that linearize the connection.

The scatterplot will be about linear if you take the logarithm of both variables because the relationship is quadratic.

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Most popular questions from this chapter

Boyle鈥檚 law If you have taken a chemistry class, then you are probably familiar with Boyle鈥檚 law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant (in symbols, PV=k). Students collected the following data on pressure and volume using a syringe and a pressure probe.

(a) Make a reasonably accurate scatterplot of the data by hand using volume as the explanatory variable.

Describe what you see.

(b) If the true relationship between the pressure and volume of the gas is PV=k, we can divide both sides of this equation by Vto obtain the theoretical model P=k/V, or P=k(1/V). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

Prey attracts predators Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the prey is low. One study looked at kelp perch and their common predator, the kelp bass. The researcher set up four large circular pens on sandy ocean bottoms off the coast of southern California. He chose young perch at random from a large group and placed 10,20,40 and60 perch in the four pens. Then he dropped the nets protecting the pens, allowing the bass to swarm in, and counted the perch left after two hours. Here are data on the proportions of perch eaten in four repetitions of this setup .

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We used Minitab software to carry out a least-squares regression analysis for these data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.

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(a) Interpret the value of SEb in context.

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(c) Interpret the interval from part (b) in context.

(d) Explain the meaning of 鈥�99% confident鈥� in context .

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(c) 1.0466卤0.2387.

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(a) If Marcella took a 7-minute shower, would it be classified as an outlier? Justify your answer.

(b) Suppose we choose 10days at random and record the length of Marcella鈥檚 shower each day. What鈥檚 the probability that her shower time is 7minutes or higher on at least 2of the days? Show your work.

(c) Find the probability that the mean length of her shower times on these 10 days exceeds5 minutes. Show your work
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