Essentials of Statistics (5th Edition)
5th Edition
ISBN: 9780321924599
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 11, Problem 1FDD
To determine
To test: The claim that the actual number of crashes agrees with the expected number of crashes.
To brief: The results obtained from the analysis.
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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 11 Solutions
Essentials of Statistics (5th Edition)
Ch. 11.2 - Prob. 1BSCCh. 11.2 - Prob. 2BSCCh. 11.2 - Prob. 3BSCCh. 11.2 - Prob. 4BSCCh. 11.2 - Prob. 5BSCCh. 11.2 - Prob. 6BSCCh. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - Prob. 9BSCCh. 11.2 - In Exercises 5-20, conduct the hypothesis test and...
Ch. 11.2 - Prob. 11BSCCh. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - Prob. 13BSCCh. 11.2 - Prob. 14BSCCh. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - Prob. 17BSCCh. 11.2 - American Idol Contestants on the TV show American...Ch. 11.2 - In Exercises 5-20, conduct the hypothesis test and...Ch. 11.2 - Prob. 20BSCCh. 11.2 - Prob. 21BSCCh. 11.2 - Prob. 22BSCCh. 11.2 - Benfords Law. According to Benfords law, a variety...Ch. 11.2 - Prob. 24BSCCh. 11.2 - Testing Goodness-of-Fit with a Normal Distribution...Ch. 11.3 - Smoking Cessation The accompanying table...Ch. 11.3 - Prob. 2BSCCh. 11.3 - Degrees of Freedom and Critical Value For the...Ch. 11.3 - Prob. 4BSCCh. 11.3 - Prob. 5BSCCh. 11.3 - Prob. 6BSCCh. 11.3 - Prob. 7BSCCh. 11.3 - Prob. 8BSCCh. 11.3 - In Exercises 5-18, test the given claim. 9. Is...Ch. 11.3 - Prob. 10BSCCh. 11.3 - In Exercises 5-18, test the given claim. 11....Ch. 11.3 - Prob. 12BSCCh. 11.3 - Soccer Strategy In soccer, serious fouls in the...Ch. 11.3 - Prob. 14BSCCh. 11.3 - Prob. 15BSCCh. 11.3 - In Exercises 5-18, test the given claim. 16....Ch. 11.3 - Prob. 17BSCCh. 11.3 - Prob. 18BSCCh. 11.3 - Prob. 19BSCCh. 11.3 - Prob. 20BSCCh. 11.3 - Prob. 21BBCh. 11.3 - Using Yatess Correction for Continuity The...Ch. 11.4 - In Exercises 1-4, use the following listed chest...Ch. 11.4 - Prob. 2BSCCh. 11.4 - In Exercises 1-4, use the following listed chest...Ch. 11.4 - Prob. 4BSCCh. 11.4 - In Exercises 516, use analysis of variance for the...Ch. 11.4 - In Exercises 516, use analysis of variance for the...Ch. 11.4 - Highway Fuel Consumption Data Set 14 in Appendix B...Ch. 11.4 - City Fuel Consumption Data Set 14 in Appendix B...Ch. 11.4 - Head Injury Crash Test Data Exercises 14 use chest...Ch. 11.4 - Pelvis Injury Crash Test Data Exercises 14 use...Ch. 11.4 - Prob. 11BSCCh. 11.4 - Prob. 12BSCCh. 11.4 - Prob. 13BSCCh. 11.4 - Prob. 14BSCCh. 11.4 - Prob. 15BSCCh. 11.4 - Prob. 16BSCCh. 11.4 - Tukey Test A display of the Bonferroni test...Ch. 11 - Prob. 1CQQCh. 11 - Prob. 2CQQCh. 11 - Questions 1-5 refer to the sample data in the...Ch. 11 - Prob. 4CQQCh. 11 - Prob. 5CQQCh. 11 - Prob. 6CQQCh. 11 - Prob. 7CQQCh. 11 - Prob. 8CQQCh. 11 - Prob. 9CQQCh. 11 - Questions 6-10 refer to the sample data in the...Ch. 11 - Auto Fatalities The table below lists auto...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Home Field Advantage Winning-team data were...Ch. 11 - Prob. 7RECh. 11 - Prob. 1CRECh. 11 - Prob. 2CRECh. 11 - ICU Patients Listed below are the ages of randomly...Ch. 11 - Prob. 4CRECh. 11 - Boats and Manatees The table below lists the...Ch. 11 - Forward Grip Reach and Ergonomics When designing...Ch. 11 - Honesty Is the Best Policy In a USA Today survey...Ch. 11 - Probability and Honesty Based on the sample...Ch. 11 - Use Statdisk, Minitab, Excel, StatCrunch, a...Ch. 11 - Prob. 1FDD
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- 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
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