Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Textbook Question
Chapter 19, Problem 11E
SECTION 16.4
11. Errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.
- a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers. They test H0: p = 0.3 vs. HA: p > 0.3 and reject the null hypothesis. Later they find out that actually 28% of all customers enrolled.
- b) A student tests 100 students to determine whether other students on her campus prefer Coke or Pepsi and finds no evidence that preference for Coke is not 0.5. Later, a marketing company tests all students on campus and finds no difference.
- c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the
mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. - d) A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by the placebo. They fail to reject the null hypothesis because the P-value is 0.465. Further testing shows that the drug actually relieves headaches in 38% of people.
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(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 19 Solutions
Intro Stats
Ch. 19.4 - 1. An experiment to test the fairness of a...Ch. 19.4 - Prob. 2JCCh. 19.4 - Prob. 3JCCh. 19.5 - Remember the bank thats sending out DVDs to try to...Ch. 19.5 - Prob. 5JCCh. 19.5 - For the bank, which situation has higher power: a...Ch. 19 - Parameters and hypotheses For each of the...Ch. 19 - Prob. 2ECh. 19 - P-values Which of the following are true? If...Ch. 19 - Prob. 4E
Ch. 19 - Prob. 5ECh. 19 - Prob. 6ECh. 19 - Prob. 7ECh. 19 - Prob. 8ECh. 19 - Prob. 9ECh. 19 - More critical values For each of the following...Ch. 19 - SECTION 16.4 11. Errors For each of the following...Ch. 19 - More errors For each of the following situations,...Ch. 19 - Prob. 13ECh. 19 - 14. Which alternative? In each of the following...Ch. 19 - CHAPTER EXERCISES 13. P-value A medical researcher...Ch. 19 - Prob. 16ECh. 19 - Alpha A researcher developing scanners to search...Ch. 19 - Prob. 18ECh. 19 - Prob. 19ECh. 19 - Significant again? A new reading program may...Ch. 19 - Prob. 21ECh. 19 - Is the Euro fair? Soon after the Euro was...Ch. 19 - 23. Approval 2011 In November 2011, Barack Obama’s...Ch. 19 - Prob. 24ECh. 19 - Prob. 25ECh. 19 - Prob. 26ECh. 19 - Prob. 27ECh. 19 - Prob. 28ECh. 19 - Prob. 29ECh. 19 - Prob. 30ECh. 19 - 31. Homeowners 2009 In 2009, the U.S. Census...Ch. 19 - Alzheimers Testing for Alzheimers disease can be a...Ch. 19 - Prob. 33ECh. 19 - Quality control Production managers on an assembly...Ch. 19 - Prob. 35ECh. 19 - 36. Production Consider again the task of the...Ch. 19 - Equal opportunity? A company is sued for job...Ch. 19 - Stop signs Highway safety engineers test new road...Ch. 19 - Prob. 39ECh. 19 - Ads A company is willing to renew its advertising...Ch. 19 - 41. Software, part II 203 students signed up for...Ch. 19 - Prob. 42ECh. 19 - Prob. 43ECh. 19 - Catheters During an angiogram, heart problems can...Ch. 19 - Prob. 45ECh. 19 - Prob. 46ECh. 19 - Prob. 47ECh. 19 - Faulty or not? You are in charge of shipping...Ch. 19 - Prob. 49ECh. 19 - Prob. 50E
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