/*! 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. R12.3 Do taller students require fewer... [FREE SOLUTION] | 91影视

91影视

Do taller students require fewer steps to walk a fixed distance? The scatterplot shows the relationship between x=height (in inches) and y=number of steps required to walk the length of a school hallway for a random sample of 36 students at a high school.

A least-squares regression analysis was performed on the data. Here is some computer output from the analysis

Long legs Do these data provide convincing evidence at the =0.05level that taller students at this school require fewer steps to walk a fixed distance? Assume that the conditions for inference are met.

Short Answer

Expert verified

We get to the conclusion that taller kids at this school take fewer steps to travel a certain distance.

Step by step solution

01

Given information

The given data is

=0.05

02

Explanation

A study was done to see if taller students needed fewer steps to go a certain distance. The scatterplot in the question depicts the link between height and the number of steps needed to walk down the school corridor. And it's been assumed that the inference requirements are met. As a result, it is assumed that

n=36

=0.05

In the row " Height" and the column "Coef" of the given computer output, the slope b1is presented as:

b1=-0.9211

In the row "Height" and the column "SE Coef" of the given computer output, the standard error of the slopeSEb1is presented as:

SEb1=0.1938

It is necessary to assert that the slope is negative.

As an example, let's define the null and alternative hypotheses as follows:

H0:=0H1:<0

The value of test statistics is now as follows:

t=b1-1SEb1

Substituting the values

t=-0.9211-00.1938

=-4.7528

Now we must calculate the P-value, for which we must first determine the degrees of freedom:

df=n-2

=36-2=34

The P-value is as follows:

P<0.0005

The null hypothesis is rejected if the P-value is less than or equal to the significance level.

P<0.05RejectH0

As a result, we get to the conclusion that taller kids at this school take fewer steps to travel a certain distance.

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 91影视!

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 32words aloud as quickly as possible, and (2) say the color in which each of 32words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (10.3) Now let's analyze the data,

a Calculate the difference (Colors-Words) (Colors - Words) for each subject and surmmarize thedistribution of differences with a boxplot. does the graph provide evidence of a difference in the average time required to perform the two tests? Explain your answer.

b. Explain why it is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks.

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 25students was selected from a large high school. For each student, x=foot length and y=height 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 the equation of the least-squares regression line for predicting height from foot length?

a. height^=10.2204+0.4117(foot length) height^=10.2204+0.4117(foot length)

b.height^=0.4117+3.0867 (foot length) height^=0.4117+3.0867(foot length)

c. height^=91.9766+3.0867(foot length) height^=91.9766+3.0867(foot length)

d. height^=91.9766+6.47044 (foot length)height^=91.9766+6.47044(foot length)

e. height^=3.0867+6.47044(foot length)heiight^=3.0867+6.47044(foot length)

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 鈥渋nverse square law,鈥 that is, a power law model of the form y=ax-2=a1x2. 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.

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥 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鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 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:

T12.4 By about how much does the sample slope typically vary from the population slope in repeated random samples of n=69 golfers?
a. 7,897,179
b. 1,698,371
c. 3,023,782
d. 281,777
e. 鈭4,139,198

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥 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鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 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:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour鈥檚 world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour鈥檚 world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of 鈭4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

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.