Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.6, Problem 1AYU
The acronym ANOVA stands for __________ __ __________.
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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 B.6 Solutions
Fundamentals of Statistics (5th Edition)
Ch. B.6 - The acronym ANOVA stands for __________ __...Ch. B.6 - True or False: To perform a one-way ANOVA, the...Ch. B.6 - True or False: To perform a one-way ANOVA, the...Ch. B.6 - The variability among the sample means is called...Ch. B.6 - The variability within each treatment group, which...Ch. B.6 - True or False: The F-test statistic is F0=MSTMSE.Ch. B.6 - In Problems 7 and 8, fill in the ANOVA table. 7.Ch. B.6 - In Problems 7 and 8, fill in the ANOVA table. 8.Ch. B.6 - In Problems 9 and 10, determine the F-test...Ch. B.6 - In Problems 9 and 10, determine the F-test...
Ch. B.6 - NW 11. The following data represent a simple...Ch. B.6 - The following data represent a simple random...Ch. B.6 - NW 13. Corn Production The data in the table...Ch. B.6 - Soybean Yield The data in the table represent the...Ch. B.6 - Which Delivery Method Is Best? At a community...Ch. B.6 - Births by Day of Week An obstetrician knew that...Ch. B.6 - Rates of Return A stock analyst wondered whether...Ch. B.6 - Reaction Time In an online psychology experiment...Ch. B.6 - Car-Buying Discrimination To determine if there is...Ch. B.6 - Crash Data The Insurance Institute for Highway...Ch. B.6 - Lower Your Cholesterol Researcher Francisco...Ch. B.6 - pH in Rain An environmentalist wanted to determine...Ch. B.6 - Age and Politics Do peoples political philosophy...Ch. B.6 - Concrete Strength An engineer wants to know if the...Ch. B.6 - Analyzing Journal Article Results Researchers...Ch. B.6 - Prob. 27AYUCh. B.6 - Diversity and pH The following data represent the...Ch. B.6 - Another E-Cig Study In a study of adult smokers...Ch. B.6 - What are the requirements to perform a one-way...Ch. B.6 - What is the mean square due to treatment estimate...Ch. B.6 - Why does a large value of the F statistic provide...Ch. B.6 - In a one-way ANOVA, explain what it means to...
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- What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forwardThere are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.arrow_forwardshow all stepsarrow_forward
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- uppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state offers the lowest premium? Which state offers the highest premium?arrow_forwardWing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 58% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 86% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(B|Ac). Round your answer to the nearest hundredth.arrow_forwardYou draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. If you get a3on the first card, find the probability of drawing a 3 for the second card.arrow_forward
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