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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

An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7years with standard deviation 2years. Do these data provide convincing evidence that the mean time of employment M for the population of postal employees has changed from the value of 7.5 that was true 20years ago? To determine this, we test the hypotheses H0:渭=7.5versus Ha:渭鈮�7.5using a one-sample ttest. What conclusion should we draw at the 5%significance level?

(a) There is convincing evidence that the mean time working with the postal service has changed.

(b) There is not convincing evidence that the mean time working with the postal service has changed.

(c) There is convincing evidence that the mean time working with the postal service is still 7.5 years.

(d) There is convincing evidence that the mean time working with the postal service is now 7years.

(e) We cannot draw a conclusion at the 5% significance level. The sample size is too small.

Significance tests A test ofH0:p=0.5versus Ha : p >0.5 has test statistic z=2.19.

(a) What conclusion would you draw at the 5 % significance level? At the 1 % level?

(b) If the alternative hypothesis were H0:p鈮�0.5what conclusion would you draw at the 5% significance level? At the 1 % level?

A random sample of 100likely voters in a small city produced 59voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0:p=0.5versus the alternative hypothesis Ha:p=0.5is

(a)z=0.59-0.50.59(0.41)100

(b). z=0.59-0.50.5(0.5)100

(c). z=0.5-0.590.59(0.41)100

(d). z=0.5-0.590.5(0.5)100

(e).t=0.59-0.50.5(0.5)100

A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal鈥檚 claim at the 伪=0.05 significance level.

Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests 500subjects. Four of these subjects do significantly better P<0.01than random guessing.

(a) Is it proper to conclude that these four people have ESP? Explain your answer.

(b) What should the researcher now do to test whether any of these four subjects have ESP?
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