Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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. 20 (page 792)

Pencils and GPA Is there a relationship between a student’s GPA and the number of pencils in his or her backpack? Jordynn and Angie decided to find out by selecting a random sample of students from their high school. Here is computer output from a least-squares regression analysis using $x =$ number of pencils and $y = GPA$ :
Is there convincing evidence of a linear relationship between GPA and number of pencils for students at this high school? Assume the conditions for inference are met.

Short Answer

Expert verified

s

Step by step solution

01

Given Information

fill

02

Simplify

fill

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read $32$ words aloud as quickly as possible, and (2) say the color in which each of $32$ words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (4.2) Let's review the design of the study-

a. Explain why this was an experiment and not an observational study.

b. Did Mr. Stames use a completely randomized design a: randomizéd black design? Why do you think he choose this experimental design?

c. Explain the purpose of the ramdom assignment in the context of the study.

Here are the data from Mr. Stames's experiment. For each subject, the time to perform the Iwo tasks is given to the nearest second.

Brawn versus brain How is the weight of an animal’s brain related to the weight of its body? Researchers collected data on the brain weight (in grams) and body weight (in Page Number: 813 Page Number: 814 kilograms) for $96$ species of mammals. The following figure is a scatterplot of the logarithm of brain weight against the logarithm of body weight for all $96$ species. The least-squares regression line for the transformed data is

${logy}^{\land} = 1.01 + 0.72 {logx}^{\hat{\log y}} = 1.01 + 0.72 \log x$

Based on footprints and some other sketchy evidence, some people believe that a large ape-like animal, called Sasquatch or Bigfoot, lives in the Pacific Northwest. Bigfoot’s weight is estimated to be about $127$ kilograms (kg). How big do you expect Bigfoot’s brain to be?

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.8 Which of the following would make the calculation in Exercise T12.7 invalid?

a. If the scatterplot of the sample data wasn’t perfectly linear.

b. If the distribution of earnings has an outlier.

c. If the distribution of earnings wasn’t approximately Normal.

d. If the earnings for golfers with small putting averages was much more variable than the earnings for golfers with large putting averages.

e. If the standard deviation of earnings is much larger than the standard deviation of putting average.

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$ students was selected from a large high school. For each student, $x = f o o t l e n g t h & y = h e i g h t$ were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a $95 %$ confidence interval for the population slope $β_{1}$ ?

a. $3.0867 \pm 0.4117$

b. $3.0867 \pm 0.8518$

c. $3.0867 \pm 0.8069$

d. $3.0867 \pm 0.8497$

e.localid="1654193042763" $3.0867 \pm 0.8481$

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean $4.5$ minutes and standard deviation $0.9$ minutes.

a. Find the probability that Marcella’s shower lasts between $3$ and $6$ minutes on a randomly selected day.

b. If Marcella took a $7$ minute shower, would it be classified as an outlier by the $1.5 I Q R$ rule? Justify your answer.

c. Suppose we choose $10$ days at random and record the length of Marcella’s shower each day. What’s the probability that her shower time is $7$ minutes or greater on at least $2$ of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds $5$ minutes.

See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

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.

Sign-up for free