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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

Refer to Exercise 28. Do the data provide convincing evidence of a difference in the distributions of opinions about how high schools are doing among black, Hispanic, and white parents?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work.

North Carolina State University studied student performance in a course required by its chemical engineering major. One question of interest was the relationship between time spent in extracurricular activities and whether a student earned a C or better in the course. Here are the data for the 119 students who answered a question about extracurricular activities:

(a) Calculate percentages and draw a bar graph that describes the nature of the relationship between time spent on extracurricular activities and performance in the course. Give a brief summary in words.

b) Explain why you should not perform a chi-square test in this setting.

Benford鈥檚 lawFaked numbers in tax returns, invoices, or expense account claims often display patterns that aren鈥檛 present in legitimate records. Some patterns are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the 铿乺st digits of numbers in legitimate records often follow a model known as Benford鈥檚 law.3 Call the 铿乺st digit of a randomly chosen record X for short. Benford鈥檚 law gives this probability model for X (note that a 铿乺st digit can鈥檛 be 0):

A forensic accountant who is familiar with Benford鈥檚 law inspects a random sample of invoices from a company that is accused of committing fraud. The table below displays the sample data.

(a) Are these data inconsistent with Benford鈥檚 law? Carry out an appropriate test at the 伪=0.05level to support your answer. If you 铿乶d a signi铿乧ant result, perform follow-up analysis.

(b) Describe a Type I error and a Type II error in this setting, and give a possible consequence of each. Which do you think is more serious?

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) 99.

Let鈥檚 continue our analysis of Joey鈥檚 sample of M&M鈥橲 Peanut Chocolate Candies from the previous Check Your Understanding (page 681).

3. Use Table C to find the P-value. Then use your calculator鈥檚 饾挸2cdf command.
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