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Chapter 9: Q. 68. (page 606)

Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. To be sure the supplier honored the terms of the agreement, the retailer had an audit performed on a random sample of 25 invoices. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.17 For example, a data value

of 38 means that the price would be lower with a different supplier for 38% of the items on the invoice. A histogram and some numerical summaries of the data are shown here. The retailer would like to determine if there is convincing evidence that the mean percent of purchases for which an alternative supplier offered lower prices is greater than 50% in the population of this company鈥檚 invoices.

a. State appropriate hypotheses for the retailer鈥檚 test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.

Short Answer

Expert verified

Part a)H0:渭<50H1:渭>50

Part b) Large sample condition is not satisfied.

Step by step solution

01

Part a) Step 1: Given information 

The claim is that mean is bigger than50%

02

Part a) Step 2: The objective is to explain the state appropriate hypothesis for the retailer's test 

The null hypothesis statement states that the population value is equal to the claim value:

H0:渭<50

The null hypothesis or the alternative hypothesis is the claim. The null hypothesis asserts that the population means equals the value specified in the claim. If the claim is the null hypothesis, then the alternative hypothesis statement is the inverse of the null hypothesis.

H1:渭>50

渭denotes the average percentage of purchases for which an alternative supply provided lower prices.

03

Part b) Step 1: Given information

Given:

04

Part b) Step 2: The objective is to find the condition for performing the test in part (a) are met. 

Random, independent (10%condition), and Normal/ Large samples are the three conditions.

Random: Satisfied because the sample was chosen at random.

Independent: Satisfied, because the sample of 25invoices represents less than 10%of the total population of invoices.

Normal/large sample size: Not happy because the sample size of 25invoices is small and the distribution is skewed (as the highest bar in the histogram is to the right in the histogram).

Because the Normal/Large sample condition is not met, a hypothesis test for the population mean is not appropriate.

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Most popular questions from this chapter

Don't argue Refer to Exercise 2. Yvonne finds that 96 of the 150 students (64%) say they rarely or never argue with friends. A significance test yields a P-value of0.0291 Interpret the P-value.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p鈮�0.25. Which of the following is an appropriate conclusion for them to draw at the 伪=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

Potato chips A company that makes potato chips requires each shipment of

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A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by

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b. using伪=0.05 instead of 伪=0.05

c. using 伪=0.05instead of 伪=0.01

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e. using a two-sided test instead of a one-sided test.

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observations from a Normal population. What values of the t statistic are statistically significant at the 伪=0.005 level?

a.t>3.326b.t>3.286c.t>2.977d.t<鈭�3.326ort>3.326e.t<鈭�3.286ort>3.286
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