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Q112S

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Statistics For Business And Economics

Found in: Page 442

Book edition 13th

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

Pages 888 pages

ISBN 9780134506593

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Short Answer

If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you want $a$ to be small or large? Explain

The firm would want $a$ to be small.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given information

The rejection of the null hypothesis of a particular test would cause a firm to go out of business.

State level of significance

Significance level $(a)$ :

The level of significance is the size of the type I error. In other words, rejecting the null hypothesis when it is true.

i.e., $a = P (r e j e c t H_{0} / H_{0} i s t r u e)$

Explain about the a, is small or large

If a null hypothesis rejection resulted in a farm going out of business, that firm would put in significant effort ensuring that it does not falsely identify a null hypothesis as correct. So, which is a type I error. Since, $a$ symbolizes this type I error.

Hence, the firm would want $a$ to be small.

Most popular questions for Math Textbooks

Ages of cable TV shoppers. Cable TV’s Home Shopping Network (HSN) reports that the average age of its shoppers is 52 years. Suppose you want to test the null hypothesis,\({H_0}:\mu = 52\), using a sample of\(n = 50\) cable TV shoppers.

a. Find the p-value of a two-tailed test if \(\overline x = 53.3\) and \(s = 7.1\)

b. Find the p-value of an upper-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)

c. Find the p-value of a two-tailed test if \(\overline x = 53.3\)and \(s = 10.4\)

d. For each of the tests, parts a–c, give a value of \(\alpha \) that will lead to a rejection of the null hypothesis.

e. If\(\overline x = 53.3\), give a value of s that will yield a two-tailed p-value of 0.01 or less.

Question: Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a Pew Internet & American Life Project Survey (October 2010). In a representative sample of 755 adults who use the Internet, 506 admitted

that they have paid to download music. Let p represent the true proportion of all Internet-using adults who have paid to download music.

a. Compute a point estimate of p.

b. Set up the null and alternative hypotheses for testing whether the true proportion of all Internet-using adults who have paid to download music exceeds.7.

c. Compute the test statistic for part b.

d. Find the rejection region for the test if α = 0.01.

e. Find the p-value for the test.

f. Make the appropriate conclusion using the rejection region.

g. Make the appropriate conclusion using the p-value.

A random sample of 175 measurements possessed a mean $\bar{x} = 8.2$ and a standard deviation s = .79.

a. Test $H_{0} : μ = 8.3$ against $H_{a} : μ \neq 8.3$ Use $a = 0.05$

Question: The hot tamale caper. “Hot tamales” are chewy, cinnamonflavored candies. A bulk vending machine is known to dispense, on average, 15 hot tamales per bag with a standard deviation of 3 per bag. Chance (Fall 2000) published an article on a classroom project in which students were required to purchase bags of hot tamales from the machine and count the number of candies per bag. One student group claimed they purchased five bags that had the following candy counts: 25, 23, 21, 21, and 20. These data are saved in the file. There was some question as to whether the students had fabricated the data. Use a hypothesis test to gain insight into whether or not the data collected by the students were fabricated. Use a level of significance that gives the benefit of the doubt to the students

Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 6.38 (p. 350). Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and that the amount of dioxide (milligrams/liter)—a measure of biodegradation—as well as presence of oil were determined for each specimen. These data are reproduced in the accompanying table.

a. Conduct a test to determine if the true mean amount of dioxide present in water specimens that contained oil was less than 3 milligrams/liter. Use \(\alpha = .10\)

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