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Chapter 11: Q. 45 (page 727)

Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. Here are data on attitudes toward coffee filters made of recycled paper from a random sample of adults:

(a) Make a bar graph that compares buyers鈥� and non-buyers鈥� opinions about recycled filters. Describe what you see

(b) Minitab output for a chi-square test using these data is shown below. Carry out the test. What conclusion do you draw?

Short Answer

Expert verified

(a) The bar graph is

Buyers frequently believe that product quality is higher, but nonbuyers frequently believe that product quality is lower.

(b) There is sufficient evidence that there is an association between the variables.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

Part (b) Step 2: Explanation

The proportions in each group is the number of subjects divided by the row total:

Create a histogram

The width of each bar is equal and the height is equal to the proportion.

Buyers frequently believe that product quality is higher, but nonbuyers frequently believe that product quality is lower.

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

The null hypothesis states that there is no association between the variables:

H0: There is no association between the variables

The alternative hypothesis states that there is an association between the variables:

Ha: There is an association between the variables

The P-value is given in the output as:

P=0.022

If the P-value is smaller than the significance level, reject the null hypothesis:

P<0.05鈬�RejectH0

There is sufficient evidence that there is an association between the variables.

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Most popular questions from this chapter

A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: (1) advise and possibly separate the couple, (2) issue a citation to the offender, and (3) arrest the offender. Police officers were trained to recognize eligible cases. When presented with an eligible case, a police officer called the dispatcher, who would randomly assign one of the three available treatments to be administered. There were a total of 650 cases in the study. Each case was classified according to whether the abuser was subsequently arrested within six months of the original incident.

(a) Explain the purpose of the random assignment in the design of this study.

(b) Construct a well-labeled graph that is suitable for comparing the effectiveness of the three treatments.

(c) We want to use these data to perform a test ofH0:p1=p2=p3wherepi=

the true proportion of spouse abusers like the ones in this study who would be arrested again within six months after receiving treatment \(i\). State an appropriate alternative hypothesis.

(d) Assume that all the conditions for performing the test in part (b) are met. The test yields 蠂2=5.063and a P-value of 0.0796Interpret this P-value in context. What conclusion should we draw from the study?

Reading and grades (10.2) Summary statistics for the two groups from Minitab are provided below.

(a) Explain why it is acceptable to use two-sample t procedures in this setting.

(b) Construct and interpret a 95% confidence interval for the difference in the mean English grade for light and heavy readers.

(c) Does the interval in part (b) provide convincing evidence that reading more causes an increase in students鈥� English grades? Justify your answer.

Market research Before bringing a new product to market, firms carry out extensive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent. The participants are a random sample of people who don鈥檛 currently use the established brand that the new product will compete with. Give subjects free samples of both detergents. After they have tried both for a while, ask which they prefer. The answers may depend on other facts about how people do laundry.

(a) How are laundry practices (water hardness and wash temperature) related to the choice of detergent? Make an appropriate graph to display this relationship. Describe what you see.

(b) Determine whether or not the sample provides convincing evidence that laundry practices and product preference are independent in the population of interest

Stress and heart attack You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say: One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only three of the 33people in the stress management group suffered 鈥渃ardiac events,鈥� defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34people in the exercise group and 12out of the 40 patients in usual care suffered such events.36

(a) Use the information in the news article to make a two-way table that describes the study results.

(b) What are the success rates of the three treatments in preventing cardiac events?

(c) Is there a significant difference in the success rates for the three treatments? Give appropriate statistical evidence to support your answer.

Many popular businesses are franchises鈥攖hink of McDonald鈥檚. The owner of local franchise benefits from brand recognition, national advertising, and detailed guidelines provided by the franchise chain. In return, he or she pays fees to the franchise firm and agrees to follow its policies. The relationship between the local owner and the franchise firm is spelled out in a detailed contract.

One clause that the contract may or may not contain is the entrepreneur鈥檚 right to an exclusive territory. This means that the new outlet will be the only representative of the franchise in a specified territory and will not have to compete with other outlets of the same chain. How does the presence of an exclusive-territory clause in the contract relate to the survival of the business?

A study designed to address this question collected data from a random sample of 170new franchise firms. Two categorical variables were measured for each franchisor. First, the franchisor was classified as successful or not based on whether or not it was still offering franchises as of a certain date. Second, the contract each franchisor offered to franchisees was classified according to whether or not there was an exclusive-territory clause. Here are the count data, arranged in a two-way table:

role="math" localid="1650453920307" Exclusive TerritorySuccessYesNoTotalYes10815123No341347Total14228170

Do these data provide convincing evidence of an association between an exclusive territory clause and business survival? Carry out an appropriate test at the 伪=0.01level.
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