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130E

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Statistics For Business And Economics

Found in: Page 132

Book edition 13th

Author(s) James T. McClave, P. George Benson, Terry Sincich

Pages 888 pages

ISBN 9780134506593

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Short Answer

Spreading rate of spilled liquid. A contract engineer atDuPont Corp. studied the rate at which a spilled volatileliquid will spread across a surface (Chemical EngineeringProgress, January 2005). Assume 50 gallons of methanol
spills onto a level surface outdoors. The engineer used derived empirical formulas (assuming a state of turbulent-freeconvection) to calculate the mass (in pounds) of the spillafter a period of time ranging from 0 to 60 minutes. The calculatedmass values are given in the table. Is there evidenceto indicate that the mass of the spill tends to diminish astime increases?
Support your answer with a scatterplot.

There is evidence that with time mass of the spill diminishes.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Interpreting whether the mass of the spill decreases with an increase in time

Looking at the data in the table, we can say that as time increases, the mass of the spill reduces.

But to make it easier to identify, we will create a scatterplot of the data from the table. We will plot the time on the x-axis and the mass on the y-axis.

The graph is given below:

Looking at the downward slope of the graph makes it easier to identify a negative correlation between the time and mass of the spill.

The downward sloping graph is evidence that the mass of the spill diminishes as time increases.

Most popular questions for Math Textbooks

Products “Made in the USA.” “Made in the USA” is a claim stated in many product advertisements or on product labels. Advertisers want consumers to believe that the product is manufactured with 100% U.S. labor and materials—which is often not the case. What does “Made in the USA” mean to the typical consumer? To answer this question, a group of marketing professors conducted an experiment at a shopping mall (Journal of Global Business, spring 2002). They asked every fourth adult entrant to the mall to participate in the study. A total of 106 shoppers agreed to answer the question, “‘Made in the USA’ means what percentage of U.S. labor and materials?” The responses of the 106 shoppers are summarized as follows: “100%” (64 shoppers), “75 to 99%” (20 shoppers), “50 to 74%” (18 shoppers), and “less than 50%” (4 shoppers).

a. What type of data-collection method was used?

b. What type of variable, quantitative or qualitative, is measured?

c. Present the data in graphical form. Use the graph to make a statement about the percentage of consumers who believe “Made in the USA” means 100% U.S. labor and materials.

Construct a scattergram for the data in the following table.

Variable 1: 174 268 345 119 400 520 190 448 307 252

Variable 2: 8 10 15 7 22 31 15 20 11 9

Question: Performance of stock screeners. Refer to the American Association of Individual Investors (AAII) statistics on stock screeners, Exercise 2.44 (p. 95). Annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners are reproduced in the table.

(9.0, -.1, -1.6, 14.6, 16.0, 7.7, 19.9, 9.8, 3.2, 24.8, 17.6, 10.7, 9.1)

a. Find the range of the data for the 13 stock screeners. Give the units of measurement for the range.

b. Find the variance of the data for the 13 stock screeners. If possible, give the units of measurement for the variance.

c. Find the standard deviation of the data for the 13 stock screeners. Give the units of measurement for the standard deviation

Calculate the mode, mean, and median of the following data:

18 10 15 13 17 15 12 15 18 16 11

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of transformer voltage sags and swells, Exercise 2.76 (p. 110). Recall that for a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.

a. Find the z-score for the number of sags for this transformer. Interpret this value.

b. Find the z-score for the number of swells for this transformer. Interpret this value.

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