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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 βof 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

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 α=0.05 level.

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

The slope β of the population regression line describes

(a) the exact increase in the selling price of an individual unit when its appraised value increases by \(1000

(b) the average increase in the appraised value in a population of units when the selling price increases by \)51000.

(c) the average increase in selling price in a population of units when the appraised value increases by \( 1000.

(d) the average selling price in a population of units when a unit's appraised value is 0.

(e) the average increase in appraised value in a sample of 16 units when the selling price increases by \) 1000.

The swinging pendulum Mrs. Hanrahan’s precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulum’s length and its period is

period=2πglength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

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

Boyle’s law Refers to Exercise 34. Here is Minitab output from separate regression analyses of the two sets of transformed pressure data:

Do each of the following for both transformations.

(a) Give the equation of the least-squares regression line. Define any variables you use.

(b) Use the model from part (a) to predict the pressure in the syringe when the volume is 17 cubic centimeters. Show your work.

(c) Interpret the value of s in context.

Suppose a name-brand drug has been deemed effective for reducing hypertension (high blood pressure). The developing company gets to keep a patent on the drug for a specific period of time before other companies can develop a generic form of the drug. Suppose the patent period is about to expire, and another company produces a generic version of this drug. The Food and Drug Administration (FDA) wants to know whether the generic drug is at least as effective as the name-brand drug in reducing blood pressure.

The following hypotheses will be used:

H0:μg=μnvs Ha:μg<μn

where

μg=true mean reduction in blood pressure using the generic drug

μn=true mean reduction in blood pressure using the name-brand drug. In the context of this situation, which of the following describes a Type I error?

(a) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(b) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does.

(c) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(d) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does.

(e) The FDA does not find sufficient evidence that the generic drug is as effective in reducing blood pressure as the name-brand drug when, in fact, it is.
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