An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Textbook Question
Chapter 4.18, Problem 13E
Refer to Exercise 4.11.
- a. Are events A and B mutually exclusive?
- b. Are events A and C mutually exclusive?
- c. Are events B and C mutually exclusive?
4.11 Refer to Exercise 4.10. Assume that the die is a fair die, that is, each of the outcomes has a probability of 1/36. What is the probability of observing
- a.
Event A: Exactly one dot appears on each of the two upturned faces? - b. Event B: The sum of the dots on the two upturned faces is exactly 4?
- c. Event C: The sum of the dots on the two upturned faces is at most 4?
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Students have asked these similar questions
(c) Because logistic regression predicts probabilities of outcomes, observations used to build a logistic regression model need not be independent.
A. false: all observations must be independent
B. true
C. false: only observations with the same outcome need to be independent
I ANSWERED: A. false: all observations must be independent.
(This was marked wrong but I have no idea why. Isn't this a basic assumption of logistic regression)
Business discuss
Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output:
Estimate
SE
Z
Pr(>|Z|)
(Intercept)
-0.8161
0.086
-9.4895
0
to_multiple
-2.5651
0.3052
-8.4047
0
winner
1.5801
0.3156
5.0067
0
format
-0.1528
0.1136
-1.3451
0.1786
re_subj
-2.8401
0.363
-7.824
0
(a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…
Chapter 4 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 4.18 - Indicate which interpretation of the probability...Ch. 4.18 - If you are having a stroke, it is critical that...Ch. 4.18 - In reporting highway safety, the National Highway...Ch. 4.18 - In a cable TV program concerning the risk of...Ch. 4.18 - The gaming commission in its annual examination of...Ch. 4.18 - The state vehicle inspection bureau provided the...Ch. 4.18 - The Texas Lottery has a game, Daily 4, in which a...Ch. 4.18 - A die is rolled two times. Provide a list of the...Ch. 4.18 - Refer to Exercise 4.10. Assume that the die is a...Ch. 4.18 - Refer to Exercise 4.11. a. Describe the event that...
Ch. 4.18 - Refer to Exercise 4.11. a. Are events A and B...Ch. 4.18 - A credit union takes a sample of four mortgages...Ch. 4.18 - A nuclear power plant has double redundancy on the...Ch. 4.18 - The population distribution in the United States...Ch. 4.18 - The makers of the candy MMs report that their...Ch. 4.18 - Refer to Exercise 4.11. Compute the following...Ch. 4.18 - Prob. 19ECh. 4.18 - Prob. 20ECh. 4.18 - Refer to Exercise 4.16. Let W be the event that...Ch. 4.18 - Is it possible for events A and B to be both...Ch. 4.18 - A survey of 1,000 U.S. government employees who...Ch. 4.18 - Refer to Exercise 4.23. Define the following...Ch. 4.18 - Prob. 25ECh. 4.18 - A large corporation has spent considerable time...Ch. 4.18 - The utility company in a large metropolitan area...Ch. 4.18 - Prob. 28ECh. 4.18 - Of a finance companys loans, 1% are defaulted (not...Ch. 4.18 - Refer to Exercise 4.29. Show that the posterior...Ch. 4.18 - Prob. 31ECh. 4.18 - In Example 4.4, compute the probability that the...Ch. 4.18 - Prob. 33ECh. 4.18 - In a January 15, 1998, article, the New England...Ch. 4.18 - Prob. 35ECh. 4.18 - Classify each of the following random variables as...Ch. 4.18 - Prob. 37ECh. 4.18 - Texting while driving is a very dangerous...Ch. 4.18 - Prob. 39ECh. 4.18 - The numbers of cars failing an emissions test on...Ch. 4.18 - A traditional call center has a simple mission:...Ch. 4.18 - A biologist randomly selects 10 portions of water,...Ch. 4.18 - Examine the accompanying newspaper clipping. Does...Ch. 4.18 - A survey is conducted to estimate the percentage...Ch. 4.18 - In an attempt to decrease drunk driving, police...Ch. 4.18 - The quality control department examines all the...Ch. 4.18 - Prob. 47ECh. 4.18 - The CFO of a hospital is concerned about the risk...Ch. 4.18 - Suppose the random variable y has a Poisson...Ch. 4.18 - Customers arrive at a grocery store checkout at a...Ch. 4.18 - A firm is considering using the Internet to...Ch. 4.18 - Prob. 52ECh. 4.18 - Prob. 53ECh. 4.18 - Prob. 54ECh. 4.18 - Prob. 55ECh. 4.18 - Prob. 56ECh. 4.18 - Prob. 57ECh. 4.18 - Prob. 58ECh. 4.18 - Prob. 59ECh. 4.18 - Prob. 60ECh. 4.18 - In Exercises 4.57 through 4.63, let z be a random...Ch. 4.18 - Prob. 62ECh. 4.18 - Prob. 63ECh. 4.18 - Prob. 64ECh. 4.18 - Let y be a random variable having a normal...Ch. 4.18 - Suppose that y is a random variable having a...Ch. 4.18 - Suppose that z is a random variable having a...Ch. 4.18 - Prob. 68ECh. 4.18 - Records maintained by the office of budget in a...Ch. 4.18 - The College Boards, which are administered each...Ch. 4.18 - Monthly sales figures for a particular food...Ch. 4.18 - Refer to Exercise 4.70. An honor society wishes to...Ch. 4.18 - Prob. 73ECh. 4.18 - Prob. 74ECh. 4.18 - A psychologist is interested in studying women who...Ch. 4.18 - Prob. 76ECh. 4.18 - A random sample of 16 measurements is drawn from a...Ch. 4.18 - Prob. 78ECh. 4.18 - Psychomotor retardation scores for a particular...Ch. 4.18 - Federal resources have been tentatively approved...Ch. 4.18 - Refer to Exercise 4.80. What size facility should...Ch. 4.18 - Based on the 1990 census, the number of hours per...Ch. 4.18 - The level of a particular pollutant, nitrogen...Ch. 4.18 - Refer to Exercise 4.83. A company has a fleet of...Ch. 4.18 - The baggage limit for an airplane is set at 100...Ch. 4.18 - A patient visits her doctor with concerns about...Ch. 4.18 - Critical key-entry errors in the data processing...Ch. 4.18 - Prob. 88ECh. 4.18 - Let y be a binomial random variable with n = 10...Ch. 4.18 - Prob. 90ECh. 4.18 - A marketing research firm advises a new client...Ch. 4.18 - Prob. 92ECh. 4.18 - Suppose a population consists of the 10...Ch. 4.18 - The fracture toughness in concrete specimens is a...Ch. 4.18 - One way to audit expense accounts for a large...Ch. 4.18 - The breaking strengths for 1-foot-square samples...Ch. 4.18 - Refer to Exercise 4.96. Suppose that a new...Ch. 4.18 - Refer to Exercise 4.97. Suppose that the mean...Ch. 4.18 - Prob. 99SECh. 4.18 - Prob. 100SECh. 4.18 - Experts consider high serum cholesterol levels to...Ch. 4.18 - Prob. 102SECh. 4.18 - Prob. 103SECh. 4.18 - Prob. 104SECh. 4.18 - Prob. 105SECh. 4.18 - Prob. 106SECh. 4.18 - Refer to Exercise 4.106. Plot the sampling...Ch. 4.18 - Random samples of size 5, 20, and 80 are drawn...Ch. 4.18 - Prob. 109SECh. 4.18 - Suppose the probability that a major earthquake...Ch. 4.18 - Prob. 111SECh. 4.18 - Airlines overbook (sell more tickets than there...Ch. 4.18 - Prob. 113SECh. 4.18 - As part of a study to determine factors that may...
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