WebAssign Printed Access Card for Brase/Brase’s Understanding Basic Statistics, Single Term
WebAssign Printed Access Card for Brase/Brase’s Understanding Basic Statistics, Single Term
8th Edition
ISBN: 9781337683692
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 1, Problem 1DHGP

Use a random-number table or random-number generator to simulate tossing a fair coin 10 times. Generate 20 such simulations of 10 coin tosses. Compare the simulations. Are there any strings of 10 heads? Of 4 heads? Does it seem that in most of the simulations, half the outcomes are heads? Half are tails? In Chapter 6, we will study the probabilities of getting from 0 to 10 heads in such a simulation.

Expert Solution & Answer
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To determine

The random number generator to simulate 20 samples of 10 coins tosses and explain the comparison of simulations.

Answer to Problem 1DHGP

Solution: The 20 simulation of 10 coin tosses is obtained as:

s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20
H H T T T H H H H H T T H H T T H T H T
H H T H H T H H T T T T T T T T H H T T
T H H T T H T T H T H T T T H H T H H T
H H H T T T H T T T T T H T H T T T T T
H H T T T H H T H H T H H H T T T H H T
H H H H H T H H T T T H H T T H T T H T
H T H T H H T T T H H T H T H H T T T T
T H H T H H T T H H H H T T H H T H H H
H T H H H H H H T H H T T T T H T T T H
T T T T T T T T H H T T H H T T H H H H

It does not seem that any string has 10 heads. There are 4 strings of four heads. Only 4 strings have half heads and half tails.

Explanation of Solution

There are several ways to assign numbers to the two outcomes because coin is fair. Suppose, quarter is fair ‘0’ digit is assigned to the outcome heads (H) and ‘1’ digit to the outcome tails (T).

To simulate the outcomes of tossing a coin 10 times by using Excel as follows:

Select the cell that to use to generate the random number between 0 and 1 in Excel. Select cell A1.

Enter the formula =RANDBETWEEN(0,1) in cell A1.

This formula is then copied down from A1 to A10.

Copied these 10 cells in column B to T to obtain 20 simulations.

The 20 simulation of 10 coin tosses is obtained as:

s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20
0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1
0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1
1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1
0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1
0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1
0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1
0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1
1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0
0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0
1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0

The outcomes (H and T) associated with 20 samples as:

s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20
H H T T T H H H H H T T H H T T H T H T
H H T H H T H H T T T T T T T T H H T T
T H H T T H T T H T H T T T H H T H H T
H H H T T T H T T T T T H T H T T T T T
H H T T T H H T H H T H H H T T T H H T
H H H H H T H H T T T H H T T H T T H T
H T H T H H T T T H H T H T H H T T T T
T H H T H H T T H H H H T T H H T H H H
H T H H H H H H T H H T T T T H T T T H
T T T T T T T T H H T T H H T T H H H H

The above random sample is obtained with replacement. There is no any string (sample) of 10 heads. There are 4 samples of 4 heads. These four samples are s8, s11, s15 and s19.

There are 4 samples of 5 heads and 5 tails. These four samples are s5, s9, s16 and s18. It does not seem that in most of simulations, half the outcomes are head or tails.

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Chapter 1 Solutions

WebAssign Printed Access Card for Brase/Brase’s Understanding Basic Statistics, Single Term

Ch. 1.1 - Student Life: Levels of Measurement Categorize...Ch. 1.1 - Business: Levels of Measurement Categorize these...Ch. 1.1 - Fishing: Levels of Measurement Categorize these...Ch. 1.1 - Education: Teacher Evaluation If you were going to...Ch. 1.1 - Critical Thinking You are interested in the...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Explain the difference...Ch. 1.2 - Statistical Literacy Marcie conducted a study of...Ch. 1.2 - Statistical Literacy A random sample of students...Ch. 1.2 - Interpretation In a random sample of 50 students...Ch. 1.2 - Interpretation A campus performance series...Ch. 1.2 - Critical Thinking Greg took a random sample of...Ch. 1.2 - Critical Thinking Consider the students in your...Ch. 1.2 - Critical Thinking Suppose you are assigned the...Ch. 1.2 - Critical Thinking In each of the following...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Sampling: Random Use a random-number table to...Ch. 1.2 - Prob. 14PCh. 1.2 - Computer Simulation: Roll of a Die A die is a cube...Ch. 1.2 - Prob. 16PCh. 1.2 - Education: Test Construction Professor Gill is...Ch. 1.2 - Education: Test Construction Professor Gill uses...Ch. 1.2 - Sampling Methods: Benefits Package An important...Ch. 1.2 - Sampling Methods: Health Care Modern Managed...Ch. 1.3 - Statistical Literacy A study of college graduates...Ch. 1.3 - Statistical Literacy Consider a completely...Ch. 1.3 - Critical Thinking A brief survey regarding...Ch. 1.3 - Critical Thinking A randomized block design was...Ch. 1.3 - Interpretation Zane is examining two studies...Ch. 1.3 - Interpretation Suppose you are looking at the 2006...Ch. 1.3 - Ecology: Gathering Data Which technique for...Ch. 1.3 - General: Gathering Data Which technique for...Ch. 1.3 - General: Completely Randomized Experiment How...Ch. 1.3 - Survey: Manipulation The NewYork Times did a...Ch. 1.3 - Critical Thinking An agricultural study is...Ch. 1 - Terminology If a numerical measure describes an...Ch. 1 - Terminology If a variable describes an individual...Ch. 1 - Prob. 3CRCh. 1 - Terminology If it makes sense to say that one data...Ch. 1 - Terminology Consider a sample of size n. If every...Ch. 1 - Terminology If a treatment is applied to subjects...Ch. 1 - Critical Thinking Sudoku is a puzzle consisting of...Ch. 1 - Critical Thinking Alisha wants to Jo a statistical...Ch. 1 - Statistical Literacy You are conducting a study of...Ch. 1 - Radio Talk Show: Sample Bias A radio talk show...Ch. 1 - Prob. 11CRCh. 1 - General: Type of Sampling Categorize the type of...Ch. 1 - General: Gathering Data Which technique fur...Ch. 1 - General: Experiment How would you use a completely...Ch. 1 - Student Life: Data Collection Project Make a...Ch. 1 - Form Problem: Fireflies Suppose you air conducting...Ch. 1 - Use a random-number table or random-number...Ch. 1 - Use a random-number table or random-number...Ch. 1 - What does it mean to say that we are going to use...Ch. 1 - In your own words, explain the differences among...Ch. 1 - Simulate the results of tossing a fair die 18...Ch. 1 - Prob. 2UTA
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