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Chapter 9: Q.2.1 (page 558)

According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. In a national survey of restaurant employees, 75% said that work stress had a negative impact on their personal lives. 11 Managers of a large restaurant chain wonder whether this national result holds for their employees. A random sample of 100 employees finds that 68 answered "Yes" when asked, "Does work stress have a negative impact on your personal life?" Is this good reason to think that the proportion of all employees in this chain who would say "Yes" differs from the national proportion of 0.75? Support your answer with a significance test.

Short Answer

Expert verified

Yes the proportion of all employees in this chain who would say "Yes" differs from the national proportion of0.75 as there is enough evidence to support this.

Step by step solution

01

Introduction

Work pressure can be characterized as the destructive physical and close to home reactions that happen when the necessities of the gig don't match the abilities, assets, or requirements of the labourer. Work pressure can prompt chronic weakness and even injury.

02

Explanation

The sample size is n = 100

Confidence level is 95%

population proportion is 0.75

Calculating the null and alternative hypotheses

H0:p=0.75Ha:p鈮�0.75

Using a calculator we get the p-value is larger than the significance level.

Hence, the null hypothesis is not rejected and there is enough evidence to support this.

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Most popular questions from this chapter

Ages of presidents Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to perform a significance test about the mean age of all U.S. presidents. Explain why this makes no sense.

An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor鈥檚 lawyer wants to compare the broker鈥檚 performance against the market as a whole. He collects data on the broker鈥檚 returns for a

random sample of 36 weeks. Over the 10-year period that the broker has managed portfolios, stocks in the Standard & Poor鈥檚 500 index gained an average of 0.95% per month. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.

(a) Determine whether there are any outliers. Show your work.

(b) Interpret the P-value in context.

(c) Do these data give convincing evidence to support the lawyer鈥檚 case? Carry out a test to help you answer this question.

Heat through the glass How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institute of Standards and Technology provides exact data on properties of materials. Here are measurements of the heat conductivity of 11randomly selected pieces of a particular type of glass:

1.111.071.111.071.121.081.081.181.181.181.12

Is there convincing evidence that the conductivity of this type of glass is greater than 1? Carry out a test to help you answer this question.

Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices. The original supplier filed a lawsuit claiming violation of the agreement. In defense, the retailer had an audit performed on a random sample of 25invoices. For each audited invoice, all purchases made from other suppliers were examined and compared with those offered by the original supplier. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.26For example, a data value of 38means that the price would be lower with a different supplier for 38%of the items on the invoice. A histogram and some computer output

for these data are shown below. Explain why we should not carry out a one-sample t-test in this setting.

Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. The following table displays the data on yield (lb/acre).

(a) How can the Random condition be satisfied in this study?

(b) Perform an appropriate test to help answer the research question. Assume that the Random condition is met. What conclusion would you draw?
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