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Chapter 12: Q. 5 (page 788)

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers aged 21or older with an initial BAC of 0took part in a study to find out. Each volunteer drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. A least-squares regression analysis was performed on the data using x=number of beers and y=BAC. Here is a residual plot and a histogram of the residuals. Check whether the conditions for performing inference about the regression model are met.

Short Answer

Expert verified

Normal, equal variance, random, independent, and linear are the five requirements for regression inferences.

Step by step solution

01

Step  1 : Given Information

We have to explain that whether the state for performing inference about the regression model are met or not.

02

Simplification

Normal,equalvariance,random,independent,andlineararethefiverequirementsforregressioninferences.
The reason for this is that the histogram is bell-shaped.
The reason for this is that the vertical spread of points in the residual figure is roughly the same everywhere, therefore equal variance is satisfied.
The explanation for this is that the subjects were assigned at random. Because the respondents were randomized at random, independent: satisfied. Because all points in the residual figure are centred around zero, the linear condition is satisfied.
As a result, all states or requirements have been met.

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Most popular questions from this chapter

Random assignment is part of a well-designed comparative experiment because

a. it is fairer to the subjects.

b. it helps create roughly equivalent groups before treatments are imposed on the subjects.

c. it allows researchers to generalize the results of their experiment to a larger population.

d. it helps eliminate any possibility of bias in the experiment.

e. it prevents the placebo effect from occurring.

T12.11 Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken. A researcher plots the data and finds that a linear relationship appears to hold. Here is computer output from a least-squares
regression analysis of these data. Assume that the conditions for performing inference about the slope β1of the true regression line are met.

a. Interpret each of the following in context:
i. The slope
ii. The y intercept
iii. The standard deviation of the residuals
iv. The standard error of the slope
b. Do the data provide convincing evidence of a linear relationship between dose and weight gain? Carry out a significance test at the α=0.05 level.
c. Construct and interpret a 95%confidence interval for the slope parameter

If P(A)=0.2and P(B)=0.52 and events A and B are independent, what is P(A or B)?

a. 0.1248

b. 0.28

c. 0.6352

d. 0.76

e. The answer cannot be determined from the given information.

Which of the following statements about the t distribution with degrees of freedom dfis (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom. III. III. As df increases, the t distribution approaches the standard Normal distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

Insurance adjusters are always concerned about being overcharged for accident repairs. The adjusters suspect that Repair Shop1quotes higher estimates than Repair Shop2. To check their suspicion, the adjusters randomly select 12cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to fix the vehicle. The estimates are given in hundreds of dollars.

Assuming that the conditions for inference are met, which of the following significance tests should be used to determine whether the adjusters’ suspicion is correct?

a. A pairedt test

b. A two-sample ttest

c. A t test to see if the slope of the population regression line is0

d. A chi-square test for homogeneity

e. A chi-square test for goodness of fit
See all solutions

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