Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 8.4, Problem 25E
A study was conducted to compare the
- a Estimate the difference in the mean number of police emergency calls per 8-hour shift between the two districts in the city.
- b Find a bound for the error of estimation.
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Calculate the mean for Study Hours and Test Scores.
Compute the covariance between the two variables using the formula:
Calculate the standard deviation for Study Hours (X) and Test Scores (Y).
Determine the correlation coefficient
Interpret the results: What does the calculated r-value indicate about the relationship between study hours and test scores?
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
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c. What is the probability that a…
Chapter 8 Solutions
Mathematical Statistics with Applications
Ch. 8.2 - Using the identity ()=[E()]+[E()]=[E()]+B(), Show...Ch. 8.2 - a. If is an unbiased estimator for , what is B()?...Ch. 8.2 - Suppose that is an estimator for a parameter and...Ch. 8.2 - Refer to Exercise 8.1. a. If is an unbiased...Ch. 8.2 - Refer to Exercises 8.1 and consider the unbiased...Ch. 8.2 - Suppose that E(1)=E(2)=, V(1)=12, and V(2)=22....Ch. 8.2 - Consider the situation described in Exercise 8.6....Ch. 8.2 - Suppose that Y1, Y2, Y3 denote a random sample...Ch. 8.2 - Suppose that Y1, Y2,, Yn constitute a random...Ch. 8.2 - The number of breakdowns per week for a type of...
Ch. 8.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 8.2 - The reading on a voltage meter connected to a test...Ch. 8.2 - We have seen that if Y has a binomial distribution...Ch. 8.2 - Prob. 14ECh. 8.2 - Let Y, Y2,,Yn denote a random sample of size n...Ch. 8.2 - Suppose that Y1, Y2,,Yn constitute a random sample...Ch. 8.2 - If Y has a binomial distribution with parameters n...Ch. 8.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 8.2 - Prob. 19ECh. 8.2 - Suppose that Y1, Y2, Y3, Y4 denote a random sample...Ch. 8.4 - An investigator is interested in the possibility...Ch. 8.4 - An increase in the rate of consumer savings...Ch. 8.4 - The Environmental Protection Agency and the...Ch. 8.4 - A study was conducted to compare the mean number...Ch. 8.4 - The Mars twin rovers, Spirit and Opportunity,...Ch. 8.4 - A random sample of 985 likely votersthose who are...Ch. 8.4 - In a study of the relationship between birth order...Ch. 8.4 - Sometimes surveys provide interesting information...Ch. 8.4 - Refer to Exercise 8.29. Give the point estimate...Ch. 8.4 - In a study to compare the perceived effects of two...Ch. 8.4 - An auditor randomly samples 20 accounts receivable...Ch. 8.4 - Refer to Exercise 8.32. From the data given on the...Ch. 8.4 - We can place a 2-standard-deviation bound on the...Ch. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Refer to Exercise 8.36. An engineer observes n =...Ch. 8.4 - Prob. 38ECh. 8.5 - Suppose that the random variable Y has a gamma...Ch. 8.5 - Suppose that the random variable Y is an...Ch. 8.5 - Suppose that Y is normally distributed with mean 0...Ch. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Let Y have probability density function...Ch. 8.5 - Refer to Exercise 8.44. a Use the pivotal quantity...Ch. 8.5 - Refer to Example 8.4 and suppose that Y is a...Ch. 8.5 - Refer to Exercise 8.46. Assume that Y1, Y2, , Yn...Ch. 8.5 - Prob. 48ECh. 8.6 - Refer to Example 8.8. In this example, p1 and p2...Ch. 8.6 - Prob. 51ECh. 8.6 - Prob. 52ECh. 8.6 - Prob. 53ECh. 8.6 - Prob. 54ECh. 8.6 - Prob. 55ECh. 8.6 - Is Americas romance with movies on the wane? In a...Ch. 8.6 - Refer to Exercise 8.29. According to the result...Ch. 8.6 - The administrators for a hospital wished to...Ch. 8.6 - When it comes to advertising, tweens are not ready...Ch. 8.6 - What is the normal body temperature for healthy...Ch. 8.6 - A small amount of the trace element selenium, from...Ch. 8.6 - The following statistics are the result of an...Ch. 8.6 - Most Americans love participating in or at least...Ch. 8.6 - In a CNN/USA Today/Gallup Poll, 1000 Americans...Ch. 8.6 - For a comparison of the rates of defectives...Ch. 8.6 - Historically, biology has been taught through...Ch. 8.6 - One suggested method for solving the...Ch. 8.6 - Prob. 68ECh. 8.6 - Prob. 69ECh. 8.7 - Let Y be a binomial random variable with parameter...Ch. 8.7 - A state wildlife service wants to estimate the...Ch. 8.7 - Telephone pollsters often interview between 1000...Ch. 8.7 - Refer to Exercise 8.59. How many tweens should...Ch. 8.7 - Prob. 74ECh. 8.7 - Prob. 75ECh. 8.7 - Refer to the comparison of the daily adult intake...Ch. 8.7 - Prob. 77ECh. 8.7 - Refer to Exercise 8.65. How many items should be...Ch. 8.7 - Refer to Exercise 8.66. a Another similar study is...Ch. 8.8 - Although there are many treatments for bulimia...Ch. 8.8 - The carapace lengths of ten lobsters examined in a...Ch. 8.8 - Scholastic Assessment Test (SAT) scores, which...Ch. 8.8 - Chronic anterior compartment syndrome is a...Ch. 8.8 - Organic chemists often purify organic compounds by...Ch. 8.8 - Two new drugs were given to patients with...Ch. 8.8 - The Environmental Protection Agency (EPA) has...Ch. 8.8 - Refer to Exercise 8.88. Another common...Ch. 8.8 - Do SAT scores for high school students differ...Ch. 8.8 - Seasonal ranges (in hectares) for alligators were...Ch. 8.8 - Solid copper produced by sintering (heating...Ch. 8.8 - Prob. 93ECh. 8.8 - Suppose that we obtain independent samples of...Ch. 8.9 - The EPA has set a maximum noise level for heavy...Ch. 8.9 - In Exercise 8.81, we gave the carapace lengths of...Ch. 8.9 - Suppose that S2 is the sample variance based on a...Ch. 8.9 - Prob. 98ECh. 8.9 - Prob. 99ECh. 8.9 - Industrial light bulbs should have a mean life...Ch. 8.9 - In laboratory work, it is desirable to run careful...Ch. 8.9 - The ages of a random sample of live university...Ch. 8.9 - A precision instrument is guaranteed to read...Ch. 8 - Prob. 104SECh. 8 - Prob. 105SECh. 8 - In a controlled pollination study involving Phlox...Ch. 8 - Prob. 107SECh. 8 - Prob. 108SECh. 8 - To estimate the proportion of unemployed workers...Ch. 8 - Prob. 110SECh. 8 - Prob. 111SECh. 8 - Prob. 112SECh. 8 - Prob. 113SECh. 8 - Prob. 114SECh. 8 - Prob. 115SECh. 8 - Do we lose our memory capacity as we get older? In...Ch. 8 - Prob. 117SECh. 8 - Prob. 118SECh. 8 - Prob. 119SECh. 8 - Two methods for teaching reading were applied to...Ch. 8 - Prob. 121SECh. 8 - Prob. 122SECh. 8 - Prob. 123SECh. 8 - Prob. 124SECh. 8 - Prob. 125SECh. 8 - Prob. 126SECh. 8 - Prob. 127SECh. 8 - Prob. 128SECh. 8 - Prob. 129SECh. 8 - Prob. 130SECh. 8 - Refer to Exercises 1.129 and 1.130. S2 and S2 are...Ch. 8 - Prob. 132SECh. 8 - Prob. 133SECh. 8 - Prob. 134SECh. 8 - Prob. 135SECh. 8 - Prob. 136SE
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- West 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 x 10 f(x) .05 20 30 .10 .10 40 .20 50 60 .35 .20 a. Is this probability distribution valid? - Select your answer- Explain. f(x) Σf(x) Select your answer Select your answer 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_forwardFor unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons. Months Unemployed Number Unemployed 1 1029 2 1686 3 2269 4 2675 5 3487 6 4652 7 4145 8 3587 9 2325 10 1120 Let x be a random variable indicating the number of months a person is unemployed. a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals). (x) f(x) 1 2 3 4 5 6 7 8 9 10 b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution. The input in the box below will not be graded, but may be reviewed and considered by your instructor. c. What is the probability that a person…arrow_forwardIn 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 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 4 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…arrow_forward
- 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…arrow_forwardA 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?arrow_forwardA 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)?arrow_forward
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