/*! 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} Problem 29 An exam is given to students in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 29

An exam is given to students in an introductory statistics course. What is likely to be true of the shape of the histogram of scores if: a. the exam is quite easy? b. the exam is quite difficult? c. half the students in the class have had calculus, the other half have had no prior college math courses, and the exam emphasizes mathematical manipulation? Explain your reasoning in each case.

Short Answer

Expert verified
Case(a) will produce a negatively skewed distribution. Case(b) will produce a positively skewed distribution. Case (c) will produce a bimodal distribution.

Step by step solution

01

Analysis of case (a): Exam is Easy

If the exam is quite easy, the majority of students would score high. Therefore, there would be a larger concentration of scores on the higher end of the histogram. This would result in a negatively skewed or left-skewed distribution.
02

Analysis of case (b): Exam is Difficult

On the contrary, if the exam is quite difficult, the majority of students would score low. This means the majority of the scores would be on the lower end of the scale, resulting in a positively skewed or right-skewed distribution.
03

Analysis of case (c): Mixed Backgrounds

If half the students have had calculus (presumably making them better prepared for a mathematics-based exam) and the other half has had no prior college math courses, there would likely be a bimodal distribution. This means there would be two peaks on the histogram: one for the calculus-prepared students, likely scoring higher, and one for the students with no college-level math background, likely scoring lower.

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

The article "Determination of Most Representative Subdivision" (Journal of Energy Engineering [1993]: \(43-\) 55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable \(x=\) total length of streets within a subdivision are as follows: \(\begin{array}{rrrrrrrr}1280 & 5320 & 4390 & 2100 & 1240 & 3060 & 4770 & 1050 \\\ 360 & 3330 & 3380 & 340 & 1000 & 960 & 1320 & 530 \\ 3350 & 540 & 3870 & 1250 & 2400 & 960 & 1120 & 2120 \\ 450 & 2250 & 2320 & 2400 & 3150 & 5700 & 5220 & 500 \\ 1850 & 2460 & 5850 & 2700 & 2730 & 1670 & 100 & 5770 \\ 3150 & 1890 & 510 & 240 & 396 & 1419 & 2109 & \end{array}\) a. Construct a stem-and-leaf display for these data using the thousands digit as the stem. Comment on the various features of the display. b. Construct a histogram using class boundaries of 0 to 1000,1000 to 2000, and so on. How would you describe the shape of the histogram? c. What proportion of subdivisions has total length less than 2000 ? between 2000 and 4000 ?

Stress can affect the physiology and behavior of animals, just as it can with humans (as many of us know all too well). The accompanying data on \(x=\) plasma cortisol concentration (in milligrams of cortisol per milliliter of plasma) and \(y=\) oxygen consumption rate (in milligrams per kilogram per hour) for juvenile steelhead after three 2 -min disturbances were read from a graph in the paper "Metabolic Cost of Acute Physical Stress in Juvenile Steelhead" (Transactions of the American Fisheries Society [1987]: \(257-263\) ). The paper also included data for unstressed fish. \(\begin{array}{lllllllllll}x & 25 & 36 & 48 & 59 & 62 & 72 & 80 & 100 & 100 & 137\end{array}\) \(\begin{array}{lllllllllll}y & 155 & 184 & 180 & 220 & 280 & 163 & 230 & 222 & 241 & 350\end{array}\) a. Is the value of \(y\) determined solely by the value of \(x\) ? Explain your reasoning. b. Construct a scatterplot of the data. c. Does an increase in plasma cortisol concentration appear to be accompanied by a change in oxygen consumption rate? Comment.

An article in the San Luis Obispo Tribune (November 20,2002 ) stated that \(39 \%\) of those with critical housing needs (those who pay more than half their income for housing) lived in urban areas, \(42 \%\) lived in suburban areas, and the rest lived in rural areas. Construct a pie chart that shows the distribution of type of residential area (urban, suburban, or rural) for those with critical housing needs.

The Chronicle of Higher Education (August 31 , 2001) published data collected in a survey of a large number of students who were college freshmen in the fall of 2001\. Of those surveyed, \(70.6 \%\) reported that they were attending their first-choice college, \(20.8 \%\) their secondchoice college, \(5.5 \%\) their third-choice college, and \(3.1 \%\) their fourth- or higher-choice college. Use a pie chart to display this information.

'The article "Tobacco and Alcohol Use in G-Rated Children's Animated Films" (Journal of the American Medical Association [1999]: \(1131-1136\) ) reported exposure to tobacco and alcohol use in all G-rated animated films released between 1937 and 1997 by five major film studios. The researchers found that tobacco use was shown in \(56 \%\) of the reviewed films. Data on the total tobacco exposure time (in seconds) for films with tobacco use produced by Walt Disney, Inc., were as follows: \(\begin{array}{llllllllll}223 & 176 & 548 & 37 & 158 & 51 & 299 & 37 & 11 & 165\end{array}\) \(\begin{array}{ll}74 & 92\end{array}\) \(23206 \quad 9\) Data for 11 G-rated animated films showing tobacco use that were produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox were also given. The tobacco exposure times (in seconds) for these films was as follows: \(\begin{array}{lllllllllll}205 & 162 & 6 & 1 & 117 & 5 & 91 & 155 & 24 & 55 & 17\end{array}\) Construct a comparative stem-and-leaf display for these data. Comment on the interesting features of this display.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.