Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 13.5, Problem 99E
To determine
Find the degrees of freedom for the chi-square statistic if the variable has five possible values among six populations.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012).
Excel File: data05-23.xls
Number of Cups
per Day
Number of
Responses
0
365
264
193
2
3
4 or more
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.
Round your answers to four decimal places.
a. Develop a probability distribution for x.
x
0
1
2
3
f(x)
b. Compute the expected value of x.
cups of coffee
c. Compute the variance of x.
cups of coffee squared
d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day.
Compute the expected value of y.
Compare it to the expected value of x.
The…
A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency.
Develop a probability distribution for the duration of a service call.
Duration of Call
x
f(x)
1
2
3
4
Which of the following probability distribution graphs accurately represents the data set?
Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)?
What is the probability a service call will take three hours?
A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?
A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.
x
f(x)
for x = 1, 2, or 3
a. Consider the required conditions for a discrete probability function, shown below.
f(x) ≥0
Σf(x) = 1
(5.1)
(5.2)
Does this probability distribution satisfy equation (5.1)?
Select
Does this probability distribution satisfy equation (5.2)?
Select
b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)?
c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?
Chapter 13 Solutions
Introductory Statistics (10th Edition)
Ch. 13.1 - What is meant by saying that a variable has a...Ch. 13.1 - How do you identify different chi-square...Ch. 13.1 - Prob. 3ECh. 13.1 - The t-table has entries for areas of 0.10, 0.05,...Ch. 13.1 - Prob. 5ECh. 13.1 - In Exercises 13.5-13.8, use Table VII to find the...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.2 - Why is the phrase goodness of fit used to describe...Ch. 13.2 - Prob. 10E
Ch. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - In each of Exercises 13.1813.23, we have provided...Ch. 13.2 - In each of Exercises 13.1813.23, we have provided...Ch. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - In each of Exercises 13.18-13.23, we have provided...Ch. 13.2 - In each of Exercises 13.24-13.33, apply the...Ch. 13.2 - In each of Exercises 13.24-13.3, apply the...Ch. 13.2 - In each of Exercises 13.24-13.33, apply the...Ch. 13.2 - Prob. 27ECh. 13.2 - In Each of Exercises 13.24-13.33, apply the...Ch. 13.2 - Prob. 29ECh. 13.2 - In each of Exercises 13.24-13.33, apply the...Ch. 13.2 - Prob. 31ECh. 13.2 - In each of Exercises 13.24-13.33, apply the...Ch. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - The chi-square goodness-of-fit test provides a...Ch. 13.3 - Identify the type of table that is used to group...Ch. 13.3 - What are the small boxes inside the heavy lines of...Ch. 13.3 - Suppose that bivariate data are to be grouped into...Ch. 13.3 - Identify three ways in which the total number of...Ch. 13.3 - Presidential Election. According to Dave Leip's...Ch. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - AIDS Cases. According to the Centers for Disease...Ch. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Prob. 50ECh. 13.3 - Farms. The U.S. Department of Agriculture...Ch. 13.3 - Prob. 52ECh. 13.3 - AIDS Cases. Refer to Exercise 13.47. For AIDS case...Ch. 13.3 - Prob. 54ECh. 13.3 - Prob. 55ECh. 13.3 - Prob. 56ECh. 13.3 - In each of Exercises 13.57-13.59, use the...Ch. 13.3 - In each of Exercises 13.57-13.59, use the...Ch. 13.3 - In each of Exercises 13.57-13.59, use the...Ch. 13.3 - In the exercise, you are to consider two variables...Ch. 13.3 - Prob. 61ECh. 13.4 - To decide whether two variables of a population...Ch. 13.4 - Prob. 63ECh. 13.4 - Prob. 64ECh. 13.4 - Prob. 65ECh. 13.4 - Prob. 66ECh. 13.4 - Education and Salary. Studies have shown that a...Ch. 13.4 - Identify three techniques that can he tried as a...Ch. 13.4 - Prob. 69ECh. 13.4 - Prob. 70ECh. 13.4 - In each of Exercises 13.69-13.74, we have given...Ch. 13.4 - Prob. 72ECh. 13.4 - In each of Exercises 13.69-13.74, we have given...Ch. 13.4 - Prob. 74ECh. 13.4 - Prob. 75ECh. 13.4 - Prob. 76ECh. 13.4 - Prob. 77ECh. 13.4 - Prob. 78ECh. 13.4 - In Exercises13.79-13.86, use either the...Ch. 13.4 - In Exercises 13.79-13.86, use either the...Ch. 13.4 - Prob. 81ECh. 13.4 - In Exercises 13.7913.86, use either she critical...Ch. 13.4 - In Exercises 13.7913.86, use either she...Ch. 13.4 - Prob. 84ECh. 13.4 - Prob. 85ECh. 13.4 - Prob. 86ECh. 13.4 - Prob. 87ECh. 13.4 - In Exercises 13.7913.86, use either the...Ch. 13.4 - Prob. 89ECh. 13.4 - Prob. 90ECh. 13.4 - Prob. 91ECh. 13.4 - Prob. 92ECh. 13.5 - Prob. 93ECh. 13.5 - For what purpose is a chi-square homogeneity test...Ch. 13.5 - Prob. 95ECh. 13.5 - State the null and alternative hypotheses for a...Ch. 13.5 - Prob. 97ECh. 13.5 - Prob. 98ECh. 13.5 - Prob. 99ECh. 13.5 - A chi-square homogeneity test is to be conducted...Ch. 13.5 - Prob. 101ECh. 13.5 - In Exercises 13.101-13.106, use either the...Ch. 13.5 - In Exercises 13.101-13.106, use either the...Ch. 13.5 - Prob. 104ECh. 13.5 - Prob. 105ECh. 13.5 - Prob. 106ECh. 13.5 - In each of Exercises 13.107 and 13.108 a. use the...Ch. 13.5 - In each of Exercises 13.107 and 13.108, a. use the...Ch. 13 - How do you distinguish among the infinitely many...Ch. 13 - Prob. 2RPCh. 13 - Prob. 3RPCh. 13 - Explain why a chi-square goodness-of-fit test, a...Ch. 13 - Prob. 5RPCh. 13 - Rending the expected-frequency assumptions for a...Ch. 13 - Prob. 7RPCh. 13 - Suppose that you have bivariate data for an entire...Ch. 13 - Suppose that you have bivariate data for a sample...Ch. 13 - Prob. 10RPCh. 13 - Prob. 11RPCh. 13 - Prob. 12RPCh. 13 - Prob. 13RPCh. 13 - Presidents. Refer to Problem 12. a. Find the...Ch. 13 - Prob. 15RPCh. 13 - Prob. 16RPCh. 13 - Prob. 17RPCh. 13 - Prob. 18RPCh. 13 - Prob. 19RPCh. 13 - Income and Residence. The U.S. Census Bureau...Ch. 13 - Economy in Recession? The Quinnipiac University...Ch. 13 - Prob. 22RPCh. 13 - With holding Treatment. Several years ago. a poll...Ch. 13 - Recall from Chapter 1 (see page 34) that the Focus...Ch. 13 - At the beginning of this chapter, we presented a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardWest Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. Excel File: data05-19.xls 10 20 f(x) .05 .10 11 30 40 50 60 .10 .20 .35 .20 a. Is this probability distribution valid? Yes Explain. greater than or equal to 0 f(x) Σf(x) equal to 1 b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)? c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)? d. Compute the expected value and variance of x. Expected value Variance clients per year squared clients per yeararrow_forwardReconsider the patient satisfaction data in Table 1. Fit a multiple regression model using both patient age and severity as the regressors. (a) Test for significance of regression. (b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model? (c) Has adding severity to the model improved the quality of the model fit? Explain your answer.arrow_forward
- The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85. (a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a = 0.05. (b) Construct a 95% two-sided confidence interval on μ. (c) Test the hypothesis that σ² = 11 using α = 0.05. (d) Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidence interval on σ. (f) Does the assumption of normality seem reasonable for the output voltage?arrow_forwardAnalyze the residuals from the regression model on the patient satisfaction data from Exercise 3. Comment on the adequacy of the regression model.arrow_forwardConsider the hypotheses: Hop=po H₁ppo where 2 is known. Derive a general expression for determining the sample size for detecting a true mean of 1μo with probability 1-ẞ if the type I error is a.arrow_forward
- Suppose we wish to test the hypotheses: Họ : | = 15 H₁: 15 where we know that o² = 9.0. If the true mean is really 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.10? Assume that a = 0.05.arrow_forwardTable 1 contains the data from a patient satisfaction survey for a group of 25 randomly selected patients at a hospital. In addition to satisfaction, data were collected on patient age and an index that measured the severity of illness. (a) Fit a linear regression model relating satisfaction to patient age. (b) Test for significance of regression. (c) What portion of the total variability is accounted for by the regressor variable age? Table 1: Patient Satisfaction Data Severity Observation Age (21) (x2) Satisfaction (y) 1 55 50 2 46 24 3 30 46 4 35 48 5 59 58 6 61 60 7 74 65 8 38 42 9 27 42 10 51 50 11 53 38 12 41 30 13 37 31 88 14 24 34 15 42 30 16 50 48 17 58 61 18 60 71 19 62 62 20 68 38 21 70 41 22 79 66 23 63 31 24 39 42 25 49 40 BE225222222222222222 68 77 96 80 43 44 26 88 75 57 56 88 102 88 70 43 46 56 59 26 83 75arrow_forward14 A survey is conducted to determine whether would prefer to work at home, if given the 20 office employees of a certain company chance. The overall results are shown in the first bar graph, and the results broken down by gender are presented in the second. a. Interpret the results of each graph. b. Discuss the added value in including gen- der in the second bar graph. (The second bar graph in this problem is called a side by side bar graph and is often used to show results broken down by two or more variables.) c. Compare the side by side bar graph with the two pie charts that you made for Question 6. Which of the two methods is best for comparing two groups, in your opinion? A Would you prefer to work at home? (n=20) 60 50 40 Percent 20 30 20 30 10 0 No Yes Prefer to work at home? (10 males, 10 females) 80 Percent 60 00 40 40 20- No Yes No Yes Female Malearrow_forward
- Frequency 12 Suppose that a random sample of 270 gradu- ating seniors are asked what their immediate priorities are, including whether buying a house is a priority. The results are shown in the following bar graph. a. The bar graph is misleading; explain why. b. Make a new bar graph that more fairly presents the results. Is Buying a House a Priority? 300 250 200 150 100 50 0 Yes No Undecidedarrow_forwardFrequency 11 A polling organization wants to find out what voters think of Issue X. It chooses a random sample of voters and asks them for their opinions of Issue X: yes, no, or no opinion. I organize the results in the following bar graph. a. Make a frequency table of these results (including the total number). brocb. Evaluate the bar graph as to whether it biz s b fairly represents the results. of beau no STORE TO OW! vd wob spind 550 540 500 vd 480 420 360 300 250 240 Yes No Undecided Opinion on Issue Xarrow_forwardPercent 13 A car dealer specializing in minivan sales saibe conducts a survey to find out more about who its customers are. One of the variables at the company measures is gender; the results of this part of the survey are shown in the following bar graph. pow a. Interpret these results. b. Explain whether you think the bar graph is a fair and accurate representation of this data. 70 Gender of Customers 60 50 40 30 20 10 0 Males Femalesarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY