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Chapter 7: Q137SE (page 444)

EPA limits on vinyl chloride. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey Department of Health, Hazardous Substance Fact Sheet, 2010). A major plastics manufacturer, attempting to control the amount of vinyl chloride its workers are exposed to, has given instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm. A random sample of 50 air specimens produced the following statistics: \(\overline x = 3.1\)ppm,\(s = 0.5\)ppm.

a. Do these statistics provide sufficient evidence to halt the production process? Use\(\alpha = 0.01\).

b. If you were the plant manager, would you want to use a large or a small value for\(\alpha \)the test in part a? Explain.

c. Find the p-value for the test and interpret its value

Short Answer

Expert verified

The null and the alternative hypotheses are \({H_0}:\mu = 3.0\)and \({H_a}:\mu > 3.0\)

Step by step solution

01

Given information

The information is regarding a significant plastics manufacturer attempting to control the amount of vinyl chloride its workers are exposed.

A random sample of 50 air specimens produced the following statistics

\(\overline x = 3.1\)ppm

\(s = 0.5\)ppm

02

Concept of the null and the alternative hypothesis

The alternative hypothesis of a test expresses your research鈥檚 prediction of an effect or relationship. In contrast, the null hypothesis of a test always predicts no effect or no association between variables.

03

Setting up the null and the alternative hypothesis

a.

The claim is that the mean amount of vinyl chloride in the air exceeds 3.0 ppm.

From the given information, the null and the alternative hypotheses are

Null hypothesis:

\({H_0}:\mu = 3.0\)

The mean amount of vinyl chloride in the air is 3.0 ppm

Alternative hypothesis:

\({H_a}:\mu > 3.0\)

The mean amount of vinyl chloride in the air is more significant than 3.0 ppm

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Most popular questions from this chapter

For safety reasons, calf dehorning has become a routine practice at dairy farms. A report by Europe鈥檚 Standing Committee on the Food Chain and Animal Health (SANKO) stated that 80% of European dairy farms carry out calf dehorning. A later study, published in the Journal of Dairy Science (Vol. 94,2011), found that in a sample of 639 Italian dairy farms, 515 dehorned calves. Does the Journal of Dairy Science study support or refute the figure reported by SANKO? Explain.

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)鈥攁 measure of biodegradation鈥攁s 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\(\alpha = .10\)

Question:Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting (January 2008) study of Machiavellian traits in accountants, Exercise 6.19 (p. 341). A Mach rating score was determined for each in a random sample of 122 purchasing managers, with the following results:虫虅 = 99.6 s = 12.6. Recall that a director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85.

a. Suppose you want to test the director鈥檚 claim. Specify the null and alternative hypotheses for the test.

b. Give the rejection region for the test using 伪 = 0.10.

c. Find the value of the test statistic.

d. Use the result, part c, to make the appropriate conclusion.

The opinions of employees at Asia-Pacific firms regarding fraud, bribery, and corruption in the workplace were elicited in the 2015 AsiaPacific (APAC) Fraud Survey. Interviews were conducted with a sample 1,508 employees of large APAC companies. One question concerned whether or not the employee鈥檚 company had implemented a 鈥渨histle-blower鈥� hotline鈥攖hat is, a phone number that an employee can call to report fraud or other types of misconduct without fear of retribution. The 2015 survey found that 680 of the 1,508 respondents鈥� companies had not implemented a whistle-blower hotline. In comparison, 436 of the 681 respondents in the 2013 survey reported their companies had not implemented a whistle-blower hotline.

a. TestH0:p=.5 against Ha:p<.5using data from the 2015 survey and 伪=.05Give a practical interpretation of the results.

b. Test H0:p=.5against Ha:p>.5using data from the 2013 survey and伪=.05 Give a practical interpretation of the results.

Jury trial outcomes. Sometimes, the outcome of a jury trial defies the 鈥渃ommon sense鈥� expectations of the general public (e.g., the 1995 O. J. Simpson verdict and the 2011 Casey Anthony verdict). Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null hypothesis in a jury trial is that the accused is innocent. (The status-quo hypothesis in the U.S. system of justice is innocence, which is assumed to be true until proven beyond a reasonable doubt.) The alternative hypothesis is guilt, which is accepted only when sufficient evidence exists to establish its truth. If the vote of the jury is unanimous in favor of guilt, the null hypothesis of innocence is rejected, and the court concludes that the accused murderer is guilty. Any vote other than a unanimous one for guilt results in a 鈥渘ot guilty鈥� verdict. The court never accepts the null hypothesis; that is, the court never declares the accused 鈥渋nnocent.鈥� A 鈥渘ot guilty鈥� verdict (as in the Casey Anthony case) implies that the court could not find the defendant guilty beyond a reasonable doubt

a. Define Type I and Type II errors in a murder trial.

b. Which of the two errors is the more serious? Explain.

c. The court does not, in general, know the values of 伪 and 尾 ; but ideally, both should be small. One of these probabilities is assumed to be smaller than the other in a jury trial. Which one, and why?

d. The court system relies on the belief that the value of is made very small by requiring a unanimous vote before guilt is concluded. Explain why this is so.

e. For a jury prejudiced against a guilty verdict as the trial begins, will the value of伪 increase or decrease? Explain.

f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of 尾 increase or decrease? Explain
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