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 80CP
a.
To determine
State the conclusion of the hypothesis test at a significance level of 0.05 using the 5 step process.
b.
To determine
State the assumptions needed for the conclusion to be valid.
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
7. 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.
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.
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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