Understanding Basic Statistics
8th Edition
ISBN: 9781337672320
Author: BRASE
Publisher: Cengage
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Chapter 3, Problem 15CRP
Interpretation
Wow! In Problems 5-13 you constructed a lot of information regarding the pH of west Texas groundwater based on sample data. Let's continue the investigation
Look at the ogive. What percent of the wells have a pH less than 8.15? Suppose a certain crop can tolerate irrigation water with a pH between 7.35 and 8.55. What percent of the wells could be used for such a crop?
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Chapter 3 Solutions
Understanding Basic Statistics
Ch. 3.1 - Statistical Literacy Consider the mode, median,...Ch. 3.1 - Statistical Literacy What symbol is used for the...Ch. 3.1 - Statistical Literacy Look at the formula for the...Ch. 3.1 - Statistical Literacy In order to find the median...Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Basic Computations Mean, Median, Mode Find the...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking If a data set has an even number...
Ch. 3.1 - Critical Thinking When a distribution is...Ch. 3.1 - Critical Thinking Consider the following types of...Ch. 3.1 - Critical Thinking Consider the numbers 23455 (a)...Ch. 3.1 - Critical Thinking Consider two data sets. Set...Ch. 3.1 - Interpretation A Job-performance evaluation form...Ch. 3.1 - Critical Thinking: Data Transformation Using...Ch. 3.1 - Critical Thinking: Data Transformation Using...Ch. 3.1 - Critical Thinking Consider a data set of 15...Ch. 3.1 - Environmental Studies: Death Valley How hot does...Ch. 3.1 - Ecology: Wolf Packs How large is a wolf pack? The...Ch. 3.1 - Medical: Injuries The Grand Canyon and the...Ch. 3.1 - Football: Age of Professional Players How old are...Ch. 3.1 - Leisure: Maui Vacation How expensive is Maui? It...Ch. 3.1 - Basic Computation: Weighted Average Find the...Ch. 3.1 - Basic Computation: Weighted Average Find the...Ch. 3.1 - Grades: Weighted Average In your biology class,...Ch. 3.1 - Merit Pay Scale: Weighted Average At General...Ch. 3.1 - EPA: Wetlands Where does all the water go?...Ch. 3.1 - Expand Your knowledge: Harmonic Mean When data...Ch. 3.1 - Expand Your Knowledge: Geometric Mean When data...Ch. 3.2 - Statistical Literacy Which averagemean, median, or...Ch. 3.2 - Statistical Literacy What is the relationship...Ch. 3.2 - Statistical Literacy When computing the standard...Ch. 3.2 - Statistical Literary What symbol is used for the...Ch. 3.2 - Basic Computation: Range, Standard Deviation...Ch. 3.2 - Basic Computation: Range, Standard Deviation...Ch. 3.2 - Critical Thinking Fora given data set in which not...Ch. 3.2 - Critical Thinking Consider two data sets with...Ch. 3.2 - Critical Thinking Each of the following data sets...Ch. 3.2 - Critical Thinking: Data Transformation Using...Ch. 3.2 - Critical Thinking: Data Transformation Using...Ch. 3.2 - Critical Thinking: Outliers One indicator of an...Ch. 3.2 - Basic Computation: Variance, Standard Deviation...Ch. 3.2 - Basic Computation: Coefficient of Variation,...Ch. 3.2 - Basic Computation: Coefficient of Variation....Ch. 3.2 - Investing: Stocks and Bonds Do bonds reduce the...Ch. 3.2 - Space Shuttle: Epoxy Kevlar epoxy it a material...Ch. 3.2 - Archaeology: Ireland The Hill of Tara in Ireland...Ch. 3.2 - Wildlife: Mallard Ducks and Canada Geese For...Ch. 3.2 - Investing: Socially Responsible Mutual Funds Pax...Ch. 3.2 - Medical: Physician Visits In some reports, the...Ch. 3.2 - Grouped Data: Anthropology What was the age...Ch. 3.2 - Grouped Data: Shoplifting What is the age...Ch. 3.2 - Grouped Data: Hours of Sleep per Day Alexander...Ch. 3.2 - Grouped Data: Business Administration What are the...Ch. 3.2 - Expand Your knowledge: Moving Averages You do not...Ch. 3.2 - Prob. 27PCh. 3.2 - Expand Your knowledge: Stratified Sampling and...Ch. 3.2 - Expand Your knowledge: Stratified Sampling and...Ch. 3.2 - Prob. 30PCh. 3.3 - Statistical Literacy Angela took a general...Ch. 3.3 - Statistical Literacy One standard for admission to...Ch. 3.3 - Critical Thinking The town of Butler, Nebraska,...Ch. 3.3 - Critical Thinking Clayton and Timothy took...Ch. 3.3 - Basic Computation: Five-Number Summary,...Ch. 3.3 - Basic Computation: Five-Number Summary...Ch. 3.3 - Health Care: Nurses At Center Hospital there is...Ch. 3.3 - Health Care: Staff Another survey was done at...Ch. 3.3 - Sociology: College Graduates What percentage of...Ch. 3.3 - Sociology: High School Dropouts What percentage of...Ch. 3.3 - Auto Insurance: Interpret GraphsConsumer Reports...Ch. 3.3 - Expand Your knowledge: Outliers Some data include...Ch. 3 - Terminology Consider the following measures of...Ch. 3 - Terminology Consider the statement: For a 5%...Ch. 3 - Terminology When we compute a sample standard...Ch. 3 - Terminology Consider the following terms: outlier,...Ch. 3 - Terminology Consider the following symbols: s,,x,....Ch. 3 - Terminology How is the standard deviation related...Ch. 3 - Terminology In a box-and-whisker plot. which...Ch. 3 - Terminology Consider the following statement: If...Ch. 3 - Statistical Literacy (a) What measures of...Ch. 3 - Critical Thinking Look at the two histograms on...Ch. 3 - Critical Thinking Consider the following Minitab...Ch. 3 - Consumer: Radon Gas "Radon: The Problem No One...Ch. 3 - Political Science: Georgia Democrats How...Ch. 3 - Grade: Weighted Average Professor Cramer...Ch. 3 - General: Average Weight Wright An elevator it...Ch. 3 - Agriculture: Harvest Weight of Maize The following...Ch. 3 - Focus Problem: Water Solve the focus problem at...Ch. 3 - Agriculture: Bell Peppers The pathogen...Ch. 3 - Performance Rating: Weighted Average A performance...Ch. 3 - The Story of Old Faithful is a short book written...Ch. 3 - Most academic advisors tell students to major in a...Ch. 3 - An average is an attempt to summarize a collection...Ch. 3 - Why do we need to study the variation of a...Ch. 3 - Why is the coefficient of variation important?...Ch. 3 - What is Chebyshevs theorem? Suppose you have a...Ch. 3 - Application Using the software or calculator...Ch. 3 - Consider the following measures: mean, median,...Ch. 3 - Describe how the presence of possible outliers...Ch. 3 - Consider two data sets. A and B. The sets are...Ch. 3 - You are examining two data sets involving test...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...
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- 5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward
- 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
- 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_forwardWhat 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_forward
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