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Chapter 12: Q. 3 (page 759)

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 .

The explanatory variable is the number of perch (the prey) in a confined area. The response variable is the proportion of perch killed by bass (the predator) in two hours when the bass are allowed access to the perch. A scatterplot of the data shows a linear relationship.

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.

Short Answer

Expert verified

All conditions have been satisfied.

Step by step solution

01

Given Information

Need to find whether the conditions are satisfied are not.

02

Explanation

There are five conditions for regression inference are: Linear, Independent, Normal, Equal variance, Random

Linear: Satisfied, because all points in the residual plot are centered about 0.

Independent: Satisfied, because the subjects were randomly selected from a large population.

Normal: Satisfied, because the histogram is roughly bell-shaped.

Equal variance: Satisfied, because the vertical spread of the points in the residual plot is about the same everywhere.

Random: Satisfied, because the subject was randomly selected from a large population.

Thus all conditions have been satisfied.

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Most popular questions from this chapter

Color words (4.2)Let’s review the design of the study.

(a) Explain why this was an experiment and not an observational study.

(b) Did Mr. Starnes use a completely randomized design or a randomized block design? Why do you think he chose this experimental design?

(c) Explain the purpose of the random assignment in the context of the study. The data from Mr. Starnes’s experiment are shown below. For each subject, the time to perform the two tasks is given to the nearest second.

Explain why it would be reasonable to use an exponential model to describe the relationship between the U.S. population in the years 1790 to 1880 and the number of years since 1700. Here is some Minitab output from a linear regression analysis on the transformed data.

Time at the table Refer to Exercise 14.

(a) Construct and interpret a 98% confidence interval for the slope of the population regression line. Explain how your results are consistent with the significance test in Exercise 14.

(b) Interpret each of the following in context:

(i)s

(ii) r2

(iii) The standard error of the slope

SAT Math scores In Chapter 3, we examined data on the percent of high school graduates in each state who took the SAT and the state's mean SAT Math score in a recent year. The figure below shows a residual plot for the least-squares regression line based on these data. Are the conditions for performing inference about the slope βof the population regression line met? Justify your answer.

About 1100high school teachers attended a weeklong summer institute for teaching AP classes. After hearing about the survey in Exercise 50, the teachers in the AP Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted for a sample size of 100teachers. One of the questions on the survey was Do you have any tattoos on your body?

One of the first decisions the class had to make was what kind of sampling method to use.

(a) They knew that a simple random sample was the “preferred” method. With teachers in 40different sessions, the class decided not to use an SRS. Give at least two reasons why you think they made this decision.

(b) The AP Statistics class believed that there might be systematic differences in the proportions of teachers who had tattoos based on the subject areas that they taught. What sampling method would you recommend to account for this possibility? Explain a statistical advantage of this method over an SRS.
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