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Chapter 12: Q. 56 (page 818)

Tattoos: What per cent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302adults and found 29% of respondents had at least 1 tattoo. According to the published report, “Respondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.” Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.

Short Answer

Expert verified

The random condition was not met.

Step by step solution

01

Given information

Online survey of 2302 adults and found 29% of respondents had at least 1 tattoo.

02

Explanation

Independent, Random, and Normal are the three requirements for calculating the95% confidence interval for the proportion.

The sample was acquired using a voluntary response sample, which is not representative of the entire population, hence the random condition was not met.

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Most popular questions from this chapter

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.

a. Find the critical value for a 99%confidence interval for the slope of the true regression line. Then calculate the confidence interval.

b. Interpret the interval from part (a).

c. Explain the meaning of “localid="1654184305701" 99%confident” in this context

Here is computer output from the least-squares regression analysis of the beer and blood alcohol dat

Each morning, coffee is brewed in the school workroom by one of three faculty members, depending on who arrives first at work. Mr. Worcester arrives first 10% of the time, Dr. Currier arrives first 50%of the time, and Mr. Legacy arrives first on the remaining mornings. The probability that the coffee is strong when brewed by Dr. Currier is 0.1, while the corresponding probabilities when it is brewed by Mr. Legacy and Mr. Worcester are 0.2 and 0.3, respectively. Mr. Worcester likes strong coffee!
(a) What is the probability that on a randomly selected morning the coffee will be strong?
(b) If the coffee is strong on a randomly selected morning, what is the probability that it was brewed by Dr. Currier?

After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent. The FDA will permit the generic drug to be sold as long as there isn't convincing evidence that it is less effective than the name-brand drug. For a proposed generic drug intended to lower blood pressure, the following hypotheses will be us

where

μG=true mean reduction in blood pressureusing the generic drug μG=true mean reduction in blood pressureusing the name@brand drug

μG=true mean reduction in blood pressure

using the generic drug

μG=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 convincing evidence that the generic drug is less effective, when in reality it is less effective.

b. The FDA finds convincing evidence that the generic drug is less effective, when in reality it is equally effective.

c. The FDA finds convincing evidence that the generic drug is equally effective, when in reality it is less effective.

d. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is less effective.

e. The FDA fails to find convincing evidence that the generic drug is less effective, when in reality it is equally effective.

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I. Plot the square root of the number of Cheerios against diameter.
II. Plot the cube of the number of Cheerios against diameter.
III. Plot the log of the number of Cheerios against the log of the diameter.
IV. Plot the number of Cheerios against the log of the diameter.

a. I and II
b. I and III
c. II and III
d. II and IV
e. I and IV

Nicole and Elena wanted to know if listening to music at a louder volume negatively impacts test performance. To investigate, they recruited 30volunteers and randomly assigned 10volunteers to listen to music at 30decibels, 10volunteers to listen to music at 60decibels, and 10volunteers to listen to music at 90decibels. While listening to the music, each student took a 10-question math test. Here is computer output from a least-squares regression analysis using role="math" localid="1654167255833" x=volumeand y=numbercorrect:

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Is there convincing evidence that listening to music at a louder volume hurts test performance? Assume the conditions for inference are met.
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