EP BASIC BUS.STATS-ACCESS (18 WEEKS)
14th Edition
ISBN: 9780135989005
Author: BERENSON
Publisher: PEARSON CO
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Chapter 16, Problem 33PS
To determine
Compute and interpret
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29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
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2,3,
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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?
Chapter 16 Solutions
EP BASIC BUS.STATS-ACCESS (18 WEEKS)
Ch. 16 - If you are using exponential smoothing for...Ch. 16 - Consider a nine-year moving average used to smooth...Ch. 16 - You are using exponential smoothing on an annual...Ch. 16 - Prob. 4PSCh. 16 - Prob. 5PSCh. 16 - How have stocks performed in the past? The...Ch. 16 - Prob. 7PSCh. 16 - Prob. 8PSCh. 16 - Prob. 9PSCh. 16 - Prob. 10PS
Ch. 16 - The linear trend forecasting equation for an...Ch. 16 - There has been much publicity about bounces paid...Ch. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - The data shown in the following table and stored...Ch. 16 - Prob. 17PSCh. 16 - Prob. 18PSCh. 16 - Prob. 19PSCh. 16 - Prob. 20PSCh. 16 - Prob. 21PSCh. 16 - Prob. 22PSCh. 16 - You are given an annual time series with 40...Ch. 16 - Prob. 24PSCh. 16 - Prob. 25PSCh. 16 - Prob. 26PSCh. 16 - Prob. 27PSCh. 16 - Prob. 28PSCh. 16 - Prob. 29PSCh. 16 - Using the average baseball salary from 200 through...Ch. 16 - Using the yearly amount of solar power generated...Ch. 16 - The following residuals are from a linear trend...Ch. 16 - Prob. 33PSCh. 16 - Prob. 34PSCh. 16 - Prob. 35PSCh. 16 - Prob. 36PSCh. 16 - Prob. 37PSCh. 16 - Prob. 38PSCh. 16 - Prob. 39PSCh. 16 - Prob. 40PSCh. 16 - In forecasting daily time-series data, how many...Ch. 16 - In forecasting a quarterly time series over the...Ch. 16 - Prob. 43PSCh. 16 - Prob. 44PSCh. 16 - Are gasoline prices higher during the height of...Ch. 16 - Prob. 46PSCh. 16 - Prob. 47PSCh. 16 - The file Silver-Q contains the price in London for...Ch. 16 - Prob. 49PSCh. 16 - What is a time series?Ch. 16 - What are the different components of a time-series...Ch. 16 - What is the difference between moving average and...Ch. 16 - Prob. 53PSCh. 16 - How does the least-squares linear trend...Ch. 16 - How does autoregressive modelling differ from the...Ch. 16 - What are the different approaches to choosing an...Ch. 16 - What is the major difference between using SYX and...Ch. 16 - How does forecasting for monthly or quarterly data...Ch. 16 - Prob. 60PSCh. 16 - The monthly commercial and residential prices for...Ch. 16 - The data stored in McDonalds represent the gross...Ch. 16 - Teachers’ Retirement System of the City of New...Ch. 16 - Prob. 64PS
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- 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).arrow_forward5. 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_forward
- 4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. 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_forward
- 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.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_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_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_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_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_forward
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