Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
4th Edition
ISBN: 9780133860825
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 9, Problem 121CP
To determine
Identify the given statement as true or false.
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2,3,
ample
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the
28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
27 Suppose that you have a data set of 1, 2, 2, 3,
3, 3, 4, 4, 5, and you assume that this sample
represents a population. The mean is 3 and g
the standard deviation is 1.225.10
a. Explain why you can apply the empirical
rule to this data set.
b. Where would "most of the values" in the
population fall, based on this data set?
30 Explain how you can use the empirical rule
to find out whether a data set is mound-
shaped, using only the values of the data
themselves (no histogram available).
Chapter 9 Solutions
Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
Ch. 9.1 - H0 or Ha? For parts a and b, is the statement a...Ch. 9.1 - H0 or Ha? For each of the following, is the...Ch. 9.1 - Burden of proof For a new pesticide, should the...Ch. 9.1 - Financial aid The average financial aid package...Ch. 9.1 - Low-carbohydrate diet A study plans to have a...Ch. 9.1 - Prob. 6PBCh. 9.1 - Proper hypotheses? Explain what is wrong with each...Ch. 9.1 - Prob. 8PBCh. 9.1 - P-value Indicate whether each of the following...Ch. 9.2 - Psychic A person who claims to be psychic says he...
Ch. 9.2 - Prob. 11PBCh. 9.2 - Get P-value from z For a test of H0: p = 0.50, the...Ch. 9.2 - Get more P-values from z Refer to the previous...Ch. 9.2 - Find test statistic and P-value For a test of H0:...Ch. 9.2 - Dogs and cancer A recent study4 considered whether...Ch. 9.2 - Religion important in your life? Americans ages 18...Ch. 9.2 - Prob. 17PBCh. 9.2 - Prob. 18PBCh. 9.2 - Testing a headache remedy Studies that compare...Ch. 9.2 - Gender bias in selecting managers For a large...Ch. 9.2 - Gender discrimination Refer to the 95% confidence...Ch. 9.2 - Garlic to repel ticks A study (J. Amer. Med....Ch. 9.2 - Exit-poll predictions According to an exit poll of...Ch. 9.2 - Which cola? The 49 students in a class at the...Ch. 9.2 - How to sell a burger A fast-food chain wants to...Ch. 9.2 - A binomial headache A null hypothesis states that...Ch. 9.2 - P-value for small samples Example 4, on whether...Ch. 9.3 - Which t has P-value = 0.05? A t test for a mean...Ch. 9.3 - Practice mechanics of a t test A study has a...Ch. 9.3 - Prob. 30PBCh. 9.3 - Low carbohydrate diet In a recent study,8 272...Ch. 9.3 - Prob. 32PBCh. 9.3 - Facebook friends Many students brag that they have...Ch. 9.3 - Lake pollution An industrial plant claims to...Ch. 9.3 - Weight change for controls A disadvantage of the...Ch. 9.3 - Crossover study A crossover study of 13 children...Ch. 9.3 - Too little or too much wine? Wine-pouring vending...Ch. 9.3 - Prob. 38PBCh. 9.3 - Assumptions important? Refer to the previous...Ch. 9.3 - Anorexia in teenage girls Example 8 described a...Ch. 9.3 - Sensitivity study Ideally, results of a...Ch. 9.3 - Prob. 42PBCh. 9.4 - Dr. Dog In the experiment in Example 4, we got a...Ch. 9.4 - Error probability A significance test about a...Ch. 9.4 - Fracking errors Example 6, in testing H0: p = 0.5...Ch. 9.4 - Prob. 46PBCh. 9.4 - Anorexia decision Refer to the previous exercise....Ch. 9.4 - Prob. 48PBCh. 9.4 - Errors in medicine Consider the test of H0: The...Ch. 9.4 - Prob. 50PBCh. 9.4 - Detecting prostate cancer Refer to the previous...Ch. 9.4 - Prob. 52PBCh. 9.5 - Misleading summaries? Two researchers conduct...Ch. 9.5 - Practical significance A study considers whether...Ch. 9.5 - Prob. 55PBCh. 9.5 - Fishing for significance A marketing study...Ch. 9.5 - Prob. 57PBCh. 9.5 - Prob. 58PBCh. 9.5 - Interpret medical research studies a. An...Ch. 9.6 - Find P(Type II error) A study is designed to test...Ch. 9.6 - Gender bias in selecting managers Exercise 9.20...Ch. 9.6 - Prob. 62PBCh. 9.6 - P(Type II error) large when p close to H0 For...Ch. 9.6 - Prob. 64PBCh. 9.6 - Power for infertility trial Consider Example 13...Ch. 9.6 - Exploring Type II errors Refer to the web app from...Ch. 9 - H0 or Ha? For each of the following hypotheses,...Ch. 9 - Write H0 and Ha For each of the following...Ch. 9 - Prob. 69CPCh. 9 - Free-throw accuracy Consider all cases in which a...Ch. 9 - Brown or Whitman? Californias governor election in...Ch. 9 - Prob. 72CPCh. 9 - Prob. 73CPCh. 9 - Prob. 74CPCh. 9 - Prob. 75CPCh. 9 - Start a hockey team A fraternity at a university...Ch. 9 - Prob. 77CPCh. 9 - Prob. 78CPCh. 9 - Prob. 79CPCh. 9 - Prob. 80CPCh. 9 - Prob. 81CPCh. 9 - Two ideal children? Is the ideal number of...Ch. 9 - Prob. 83CPCh. 9 - Prob. 84CPCh. 9 - Blood pressure When Vincenzo Baranellos blood...Ch. 9 - Increasing blood pressure In the previous...Ch. 9 - Tennis balls in control? When it is operating...Ch. 9 - Prob. 88CPCh. 9 - Prob. 89CPCh. 9 - CI and test Refer to the previous exercise. a. For...Ch. 9 - Prob. 91CPCh. 9 - Religious beliefs statistically significant? A...Ch. 9 - Prob. 93CPCh. 9 - Prob. 94CPCh. 9 - Prob. 95CPCh. 9 - Prob. 96CPCh. 9 - Prob. 98CPCh. 9 - Baseball home team advantage In Major League...Ch. 9 - Prob. 100CPCh. 9 - Prob. 101CPCh. 9 - Prob. 102CPCh. 9 - Prob. 103CPCh. 9 - Prob. 104CPCh. 9 - Prob. 105CPCh. 9 - Prob. 106CPCh. 9 - Prob. 107CPCh. 9 - Prob. 108CPCh. 9 - Significance Explain the difference between...Ch. 9 - More doctors recommend An advertisement by Company...Ch. 9 - Prob. 111CPCh. 9 - Bad P-value interpretations A random sample of...Ch. 9 - Prob. 113CPCh. 9 - Prob. 114CPCh. 9 - Prob. 115CPCh. 9 - Prob. 116CPCh. 9 - Prob. 117CPCh. 9 - Prob. 118CPCh. 9 - Prob. 119CPCh. 9 - Prob. 120CPCh. 9 - Prob. 121CPCh. 9 - True or false A 95% confidence interval for =...Ch. 9 - Prob. 123CPCh. 9 - Prob. 124CPCh. 9 - Prob. 125CPCh. 9 - Prob. 126CPCh. 9 - Prob. 127CPCh. 9 - Prob. 128CP
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- 8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward7. Cantelli's inequality. Let X be a random variable with finite variance, o². (a) Prove that, for x ≥ 0, P(X EX2x)≤ 02 x² +0² 202 P(|X - EX2x)<≤ (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound o√√2. (e) Generalize Cantelli's inequality to moments of order r 1.arrow_forward
- The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardThe Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forward
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