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Chapter 12: Q. 2 (page 759)

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 尾of the population regression line met? Justify your answer.

Short Answer

Expert verified

The linear requirement has not been met.

Step by step solution

01

Given Information

Need to find which requirement has not been met.

02

Explanation

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

The Linear requirement has not been met, because the residual plot contains strong curvature and thus the scatterplot is not roughly linear.

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Most popular questions from this chapter

A city wants to conduct a poll of taxpayers to determine the level of support for constructing a new city-owned baseball stadium. Which of the following is the primary reason for using a large sample size in constructing a confidence interval to estimate the proportion of city taxpayers who would support such a project?

(a) To increase the confidence level

(b) To eliminate any confounding variables

(c) To reduce nonresponse bias

(d) To increase the precision of the estimate

(e) To reduce under coverage

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 鈥減referred鈥� 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.

Inference about the slope 尾of a least-squares regression line is based on which of the following distributions?

(a) The t distribution with n-1degrees of freedom

(b) The standard Normal distribution

(c) The chi-square distribution with n-1degrees of freedom

(d) The t distribution with n-2degrees of freedom

(e) The Normal distribution with mean 渭and standard deviation蟽

The professor swims Here are data on the time (in minutes) Professor Moore takes to swim 2000 yards and his pulse rate (beats per minute) after swimming for a random sample of 23 days:

(a) Is there statistically significant evidence of a negative linear relationship between Professor Moore's swim time and his pulse rate in the population of days on which he swims 2000 yards?

Carry out an appropriate significance test at the 伪=0.05 level.

(b) Calculate and interpret a 95% confidence interval for the slope 尾of the population regression line.

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data

on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Some

regression output for these data is shown below.

Which of the following represents a 95% confidence interval for the true slope of the least-squares regression line relating the weight of a bear and its neck girth?

(a)241.710卤38.57(b)241.70卤88.94(c)20.230卤1.695(d)20.230卤3.83(e)20.230卤3.91
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