Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Textbook Question
Chapter 5, Problem 123CRE
Simulating Guessing on a Multiple-Choice Test Suppose a student takes a 10-question multiple-choice quiz, and for each question on the quiz there are five possible options. Only one option is correct. Now suppose the student, who did not study, guesses at random for each question. A passing grade is 3 (or more) correct. We wish to design a simulation to find the
a. In this simulation, the random action consists of a student guessing on a question that has five
possible answers. We will simulate this by selecting a single digit from the random number
table given in this exercise.
In this table, we will let 0 and 1 represent correct answers, and 2 through 9 will represent
incorrect answers. Explain why this is a correct approach for the exam questions with five
possible answers.
(This completes the first two steps of the simulation summary given in Section 5.4.)
b. A trial, in this simulation, consists of picking 10 digits in a row. Each digit represents one guess on a question on the exam. Write the sequence of numbers from the first trial. Also translate this to correct and incorrect answers by writing R for right and W for wrong. (This completes step 4.)
c. We are interested in knowing whether there were 3 or more correct answers chosen. Did this occur in the first trial? (This completes step 5.)
d. Perform a second simulation of the student taking this 10-question quiz by guessing randomly. Use the second line of the table given. What score did your student get? Did the
e. Repeat the trial twice more, using lines 3 and 4 of the table. For each trial, write the score and whether or not the event occurred.
f. On the basis of these four trials, what is the empirical probability of passing the exam by guessing?
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Exercise 6-6 (Algo) (LO6-3)
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.
Admissions
Probability
1,100
0.5
1,400
0.4
1,300
0.1
Click here for the Excel Data File
Required:
What is the expected number of admissions for the fall semester?
Compute the variance and the standard deviation of the number of admissions.
Note: Round your standard deviation to 2 decimal places.
1. Find the mean of the x-values (x-bar)
and the mean of the y-values (y-bar) and write/label each here:
2. Label the second row in the table using proper notation; then, complete the table. In the fifth and sixth
columns, show the 'products' of what you're multiplying, as well as the answers.
X
y
x minus x-bar y minus y-bar (x minus x-bar)(y minus y-bar)
(x minus x-bar)^2
xy
16
20
34
4-2
5 2
3. Write the sums that represents Sxx and Sxy in the table, at the bottom of their respective columns.
4. Find the slope of the Regression line: bi
=
(simplify your answer)
5. Find the y-intercept of the Regression line, and then write the equation of the Regression line.
Show your work. Then, BOX your final answer. Express your line as "y-hat equals...
Chapter 5 Solutions
Introductory Statistics
Ch. 5 - Simulation (Example 1) If we flip a coin 10 times,...Ch. 5 - Simulation Suppose you are carrying out a...Ch. 5 - Empirical versus Theoretical A Monopoly player...Ch. 5 - Empirical versus Theoretical A person was trying...Ch. 5 - Empirical versus Theoretical A student flips a...Ch. 5 - Empirical versus Theoretical A bag of candy...Ch. 5 - Medical Group A medical practice group consists of...Ch. 5 - Teacher Effectiveness A recent study found that...Ch. 5 - Probability For each of the values, state whether...Ch. 5 - Probability For each of the values, state whether...
Ch. 5 - Cards (Example 2) There are four suits: clubs ,...Ch. 5 - Playing Cards Refer to exercise 5.11 for...Ch. 5 - Guessing on Tests a. On a true/false quiz in which...Ch. 5 - Guessing on Tests Consider a multiple-choice test...Ch. 5 - Four Coin Tosses (Example 3) The sample space...Ch. 5 - Three Children The sample space shows all possible...Ch. 5 - Birthdays What is the probability that a baby will...Ch. 5 - Playing Cards If one card is selected from a...Ch. 5 - Vacations (Example 4) The Gallup poll asked...Ch. 5 - Reading The Pew Research Center asked a sample of...Ch. 5 - Marijuana Legalization (Example 5) A Gallup poll...Ch. 5 - Marijuana Legalization Use the data in exercise...Ch. 5 - Gender Discrimination in Tech (Example 6) A Pew...Ch. 5 - Gender Discrimination in Tech Use the data in...Ch. 5 - Mutually Exclusive Suppose a person is selected at...Ch. 5 - Mutually Exclusive Suppose a student is selected...Ch. 5 - Vacations (Mutually Exclusive) (Example 7)...Ch. 5 - Vacations (Not Mutually Exclusive) Refer to the...Ch. 5 - Fair Die (Example 8) Roll a fair six-sided die. a....Ch. 5 - Fair Die Roll a fair six-sided die. a. What is the...Ch. 5 - Grades Assume that the only grades possible in a...Ch. 5 - Changing Multiple-Choice Answers One of the...Ch. 5 - Commuting A college conducted a student survey to...Ch. 5 - Political Parties Political science researchers...Ch. 5 - Super Powers (Example 9) A 2018 Marist poll asked...Ch. 5 - Online Presence A 2018 Pew poll asked U.S. adults...Ch. 5 - Thumbtacks When a certain type of thumbtack is...Ch. 5 - Thumbtacks When a certain type of thumbtack is...Ch. 5 - Multiple-Choice Exam An exam consists of 12...Ch. 5 - Driving Exam A driving exam consists of 30...Ch. 5 - Equal Rights for Women (Example 10) A recent Pew...Ch. 5 - Equal Rights for Women A person is selected...Ch. 5 - Frequent Stress (Example 11) A Gallup poll asked...Ch. 5 - Frequent Stress Use the data in exercise 5.43 for...Ch. 5 - Independent? Suppose a person is chosen at random....Ch. 5 - Independent? About 12#37; of men and 10#37; of...Ch. 5 - Independent? Suppose a person is chosen at random....Ch. 5 - Independent? Ring sizes typically range from about...Ch. 5 - Equal Rights Poll (Example 12) Refer to the table...Ch. 5 - Equal Rights Poll Assume a person is selected...Ch. 5 - Hand Folding (Example 13) When people fold their...Ch. 5 - Dice When two dice are rolled, is the event “the...Ch. 5 - TV News Source and Gender (Example 14) A 2018 Pew...Ch. 5 - TV News Source and Gender Using the table in...Ch. 5 - Coin (Example 15) Imagine flipping three fair...Ch. 5 - Die Imagine rolling a fair six-sided die three...Ch. 5 - Die Sequences (Example 16) Roll a fair six-sided...Ch. 5 - Babies Assume that babies born are equally likely...Ch. 5 - Vacations (Example 17) According to a recent...Ch. 5 - Landlines and Cell Phones According to the...Ch. 5 - Cervical Cancer (Example 18) According to a study...Ch. 5 - Cervical Cancer About 8 women in 100,000 have...Ch. 5 - Rolling Sixes (Example 19) What’s the probability...Ch. 5 - Rolling a Sum of 7 What’s the probability of...Ch. 5 - Multiple-Choice Test (Example 20) A...Ch. 5 - True/False Test A true/false test has 20...Ch. 5 - Simulating Coin Flips (Example 21) a. Use the line...Ch. 5 - Simulating Rolling a Die a. Explain how you could...Ch. 5 - Law of Large Numbers Refer to Histograms A, B, and...Ch. 5 - Law of Large Numbers The table shows the results...Ch. 5 - Coin Flips Imagine flipping a fair coin many...Ch. 5 - Coin Flips, Again Refer to the following figure....Ch. 5 - Law of Large Numbers: Gambling Betty and Jane are...Ch. 5 - LLN: Grandchildren Consider two pairs of...Ch. 5 - LLN: Coin If you flip a fair coin repeatedly and...Ch. 5 - LLN: Die The graph shows the average when a...Ch. 5 - Jury Duty A jury is supposed to represent the...Ch. 5 - Left-handed Some estimates say that 10#37; of the...Ch. 5 - Simulation: Four-Sided Die a. Explain how you...Ch. 5 - Simulation: Six-Sided Die a. Explain how you could...Ch. 5 - Prob. 81CRECh. 5 - Prob. 82CRECh. 5 - Independent Variables Use your general knowledge...Ch. 5 - Independent Variables Use your general knowledge...Ch. 5 - Prob. 85CRECh. 5 - Prob. 86CRECh. 5 - Prob. 87CRECh. 5 - Prob. 88CRECh. 5 - Birthdays Suppose all the days of the week are...Ch. 5 - Pass Rate of Written Driver’s Exam In California,...Ch. 5 - Prob. 91CRECh. 5 - Reading Habits In 2016 the Pew Research Center...Ch. 5 - Prob. 93CRECh. 5 - Prob. 94CRECh. 5 - Prob. 95CRECh. 5 - Cell Phone Security A 2017 Pew Research poll found...Ch. 5 - Coin Flips Let H stand for heads and let T stand...Ch. 5 - Prob. 98CRECh. 5 - Prob. 99CRECh. 5 - Online Dating The Pew Research Center asked a...Ch. 5 - CA Bar Exam In order to practice law, lawyers must...Ch. 5 - Driving Tests In addition to behind-the-wheel...Ch. 5 - California Recidivism and Gender Women return to...Ch. 5 - Blue Eyes About 17#37; of American men have blue...Ch. 5 - Prob. 105CRECh. 5 - Prob. 106CRECh. 5 - Law of Large Numbers A famous study by Amos...Ch. 5 - Law of Large Numbers A certain professional...Ch. 5 - Climate Change and Political Party In 2016 a Pew...Ch. 5 - Climate Change and Political Party Refer to the...Ch. 5 - Prob. 111CRECh. 5 - Prob. 112CRECh. 5 - Prob. 113CRECh. 5 - Prob. 114CRECh. 5 - Prob. 115CRECh. 5 - Prob. 116CRECh. 5 - Prob. 117CRECh. 5 - Prob. 118CRECh. 5 - Prob. 119CRECh. 5 - Prob. 120CRECh. 5 - Prob. 121CRECh. 5 - Multiple-Choice Test A multiple-choice test has 10...Ch. 5 - Simulating Guessing on a Multiple-Choice Test...Ch. 5 - Simulating Guessing on a True/False Test Perform a...Ch. 5 - Red Light/Green Light A busy street has three...Ch. 5 - Soda A soda-bottling plant has a flaw in that...
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