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Chapter 9: Q. 65 (page 587)

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.

Short Answer

Expert verified

Random: 25invoices are randomly sampled. 10%rule is less than large counts.

Step by step solution

01

Given information

The original supplier filed a lawsuit claiming a violation of the agreement.

In defense, the retailer had an audit performed on a random sample of 25invoices. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded at 26.

For example, a data value of 38means that the price would be lower with a different supplier for 38%of the items on the invoice.

02

Explanation

The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded 26. The one-sample t-test is a member of the t-test family.

All the tests in the t-test family compare differences in mean scores of continuous-level (interval or ratio), normally distributed data. Unlike the independent or dependent-sample t-tests, the one-sample t-test works with only one mean score. The one-sample t-test compares the mean of a single sample to a predetermined value to determine if the sample mean is significantly greater or less than that value.

For this case, Random: 25invoices are randomly sampled. 10%rule is less than large counts.

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Most popular questions from this chapter

The most important condition for sound conclusions from statistical inference is that

(a) the data come from a well-designed random sample or randomized experiment

(b) the population distribution be exactly Normal.

(c) the data contain no outliers.

(d) the sample size be no more than 10%of the population size.

(c) the sample size be at least 30.

For the job satisfaction study described in Section 9.1, the hypotheses are

H0:渭=0Ha:渭isnotequalto0

where 渭is the mean difference in job satisfaction scores (self-paced machine-paced) in the population of assembly-line workers at the company. Data from a random sample of 18workers gave x铃�=17and sx=60

Calculate the test statistic. Show your work.

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

a).H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p鈮�0.5

(e) H0:p>0.5;Ha:p=0.5

Packaging CDs (6.2, 5.3) A manufacturer of compact discs (CDs) wants to be sure that their CDs will fit inside the plastic cases they have bought for packaging. Both the CDs and the cases are circular. According to the supplier, the plastic cases vary Normally with mean diameter 渭=4.2inchesand a standard deviation 蟽=0.05inches. The CD manufacturer decides to produce CDs with mean diameter 渭=4inches. Their diameters follow a Normal distribution with 蟽=0.1inches.

(a) Let X = the diameter of a randomly selected CD and Y = the diameter of a randomly selected case. Describe the shape, center, and spread of the distribution of the random variable X = Y. What is the importance of this random variable to the CD manufacturer?

(b) Compute the probability that a randomly selected CD will fit inside a randomly selected case.

(c) The production process actually runs in batches of 100 CDs. If each of these CDs is paired with a randomly chosen plastic case, find the probability that all the CDs fit in their cases.

During the winter months, the temperatures at the Colorado cabin owned by the Starnes family can stay well below freezing (32掳F or 0掳C) for weeks at a time. To prevent the pipes from freezing, Mrs Starnes sets the thermostat at 50掳F. The manufacturer claims that the thermostat allows variation in-home temperature of S 3掳F. Mrs Starnes suspects that the manufacturer is overstating how well the thermostat works.
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