/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 4 Beer and BAC How well does the n... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers with an initial BAC of 0drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the 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

Linear, independent, normal, equal variance, and random are the five requirements for regression inference.

As a result, all requirements have been met.

Step by step solution

01

Given Information

Sixteen volunteers with an initial BAC of 0drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below.

02

Explanation

The five requirements for regression inference are linear, independent, normal, equal variance, and random.

Linear: Satisfied since the residual plot's points are all centered around 0.

Independent: Because the respondents were distributed at random, the subjects were satisfied.

Normal: The histogram is basically bell-shaped, so I'm satisfied.

Equal variance: Satisfied since the vertical spread of the residual plot points is almost the same everywhere.

Random: Because the subjects were allocated at random, I'm satisfied.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that the relationship between a response variable y and an explanatory variable x is modelled by y=2.7(0.316)x. Which of the following scatterplots would approximately follow a straight line?

(a) A plot of y against x

(b) A plot of y against log x

(c) A plot of log y against x

(d) A plot of log y against log x

(e) None of (a) through (d)

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.

Suppose a company manufactures plastic lids for disposable coffee cups. When the manufacturing process is working correctly, the diameters of the lids are approximately Normally distributed with a mean diameter of

4 inches and a standard deviation of 0.02 inches. To make sure the machine is not producing lids that are too big or too small, each hour a random sample of 25 lids is selected and the sample mean is calculated.

(a) Describe the shape, center, and spread of the sampling distribution of the sample mean diameter, assuming the machine is working properly.

The company decides that it will shut down the machine if the sample means the diameter is less than 3.99 inches or greater than 4.01 inches since this indicates that some lids will be too small or too large for the cups. If the sample mean is less than 3.99 or greater than 4.01, all the lids from

that hour is thrown away since the company does not want to sell bad products.

(b) Assuming that the machine is working properly, what is the probability that a random sample of 25 lids will have a mean diameter less than 3.99 inches or greater than 4.01 inches? Show your work.

Additionally, to look for any trends, each hour the company records the value of the sample mean on a chart, like the one below.

One benefit of using this type of chart is that out-of-control production trends can be noticed before it is too late and lids have to be thrown away. For example, if the sample means increased in 3 consecutive samples, this would suggest that something might be wrong with the machine.

If this trend can be noticed before the sample means gets larger than 4.01, then the machine can be fixed without having to throw away any lids.

(c) Assuming that the manufacturing process is working correctly, what is the probability that the sample mean diameter will be above the desired mean of 4.00 but below the upper boundary of 4.01? Show your work.

(d) Assuming that the manufacturing process is working correctly, what is the probability that in 5 consecutive samples, 4 or 5 of the sample means will be above the desired mean of 4.00 but below the upper boundary of 4.01? Show your work.

(e) Which of the following results gives more convincing evidence that the machine needs to be shut down? Explain.

1. Getting a single sample mean below 3.99 or above 4.01 OR

2. Taking 5 consecutive samples and having at least 4 of the sample means be between 4.00 and 4.01.

(f) Suggest a different rule (other than 1 and 2 stated in part (e)) for stopping the machine before it starts producing lids that have to be thrown away. Assuming that the machine is working properly, calculate the probability that the machine will be shut down when using your rule.

A manufacturer of electronic components is testing the durability of a newly designed integrated circuit to determine whether its life span is longer than that of the earlier model, which has a mean life span of 58months. The company takes a simple random sample of 120integrated circuits and simulates normal use until they stop working. The null and alternative hypotheses used for the significance test are given by role="math" localid="1650625928506" H0:μ=5858 and Ha:μ>58The P-value for the resulting one-samplet-test is 0.035. Which of the following best describes what the P-value measures

(a) The probability that the new integrated circuit has the same life span as the current model is 0.035.

b) The probability that the test correctly rejects the null hypothesis in favor of the alternative hypothesis is 0.035.

(c) The probability that a single new integrated circuit will not last as long as one of the earlier circuits is 0.035.

(d) The probability of getting a sample statistic as far or farther from the null value if there really is no difference between the new and the old circuits is0.035.

Which of the following is a categorical variable?

(a) The weight of automobiles

(b) The time required to complete the Olympic marathon

(c) The average gas mileage of a hybrid car

(d) The brand of shampoo purchased by shoppers in a

grocery store

(e) The average closing price of a particular stock on the

New York Stock Exchange

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.