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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 12: Q.AP4.7 - Cumulative AP Practise Test (page 828)

Which of the following is a categorical variable?
a. The weight of an automobile
b. The time required to complete the Olympic marathon
c. The fuel efficiency (in miles per gallon) of a hybrid car
d. The brand of shampoo purchased by shoppers in a grocery store
e. The closing price of a particular stock on the New York Stock Exchange

Short Answer

Expert verified

A categorical variable is option

d. The brand of shampoo purchased by shoppers in a grocery store .

Step by step solution

01

Given information

Given in the question that, We need to find the a categorical variable from the options.

02

Explanation

The town council wants to know how many adults live in their community. A categorical variable categorises an individual, whereas a quantitative variable is a numerical quantity.

As a result, it is a quantitative variable in option (a) because the weight has numerical values.

It is a quantitative variable in option (b) since time has numerical values.

It is a quantitative variable in option (c) because the fuel efficiency has a numerical value.

Because the brands are not numerical, option (d) is a categorical variable.

It is a quantitative variable in option (e) since the closing price has numerical values.

As a result, option (d) is the proper choice.

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Most popular questions from this chapter

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

$μ G =$ true mean reduction in blood pressureusing the generic drug $μ G =$ true mean reduction in blood pressureusing the name@brand drug

$μ_{G} =$ true mean reduction in blood pressure

using the generic drug

$μ_{G} =$ 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.

R12.5 Light intensity In a physics class, the intensity of a 100-watt light bulb was measured by a sensor at various distances from the light source. Here is a scatterplot of the data. Note that a candela is a unit of luminous intensity in the International System of Units.

Physics textbooks suggest that the relationship between light intensity y and distance x should follow an “inverse square law,” that is, a power law model of the form $y = a x^{- 2} = a \frac{1}{x^{2}}$ . We transformed the distance measurements by squaring them and then taking their reciprocals. Here is some computer output and a residual plot from a least-squares regression analysis of the transformed data. Note that the horizontal axis on the residual plot displays predicted light intensity.

a. Did this transformation achieve linearity? Give appropriate evidence to justify your answer.
b. What is the equation of the least-squares regression line? Define any variables you use.
c. Predict the intensity of a 100-watt bulb at a distance of 2.1 meters.

Does how long young children remain at the lunch table help predict how much they eat? Here are data on a random sample of $20$ toddlers observed over several months. “Time” is the average number of minutes a child spent at the table when lunch was served. “Calories” is the average number of calories the child consumed during lunch, calculated from careful observation of what the child ate each day.

Here is some computer output from a least-squares regression analysis of these data. Do these data provide convincing evidence at the $α = 0.01 α = 0.01$ level of a linear relationship between time at the table and calories consumed in the population of toddlers?

$Predictor Coef SE Coef T P Constant 560.65 29.37 19.09 0.000 Time - 3.0771 0.8498 - 3.62 0.002 S = 23.3980 R - Sq = 42.1 % R - Sq (adj) = 38.9 %$

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains $10$ identical hummingbird feeders and fills $5$ , chosen at random, with store-bought food from concentrate and the other 5 with a mixture of sugar and water. The feeders are then randomly assigned to $10$ possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on the amount consumed?

a. A one-sample $z -$ test for a proportion

b. A two-sample $z -$ test for a difference in proportions

c. A chi-square test for independence

d. A two-sample t-test

e. A paired t-test

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers aged $21$ or older with an initial BAC of $0$ took 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

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