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Chapter 7: Q42E (page 411)

Revenue for a full-service funeral. According to the National Funeral Directors Association (NFDA), the nation's 19,000 funeral homes collected an average of \(7,180 per full-service funeral in 2014 (www.nfda.org). A random sample of 36 funeral homes reported revenue data for the current year. Among other measures, each reported its average fee for a full-service funeral. These data (in thousands of dollars) are shown in the following table.

a. What are the appropriate null and alternative hypotheses to test whether the average full-service fee of U. S. funeral homes this year is less than \)7,180?

b. Conduct the test at\(\alpha = 0.05\). Do the sample data provide sufficient evidence to conclude that the average fee this year is lower than in 2014?

c. In conducting the test, was it necessary to assume that the population of average full-service fees was normally distributed? Justify your answer

Short Answer

Expert verified

The null and the alternative hypotheses are\({H_0}:\mu = \$ 7,180\)and\({H_a}:\mu < \$ 7,180\)

Step by step solution

01

Given information

In 2014, the nation's 19,000 funeral homes collected an average of $7,180 per full-service funeral, according to the NFDA.

02

Concept of the null and the alternative hypothesis

The null hypothesis of a test always predicts no effect or no association between variables, while the alternative hypothesis states your research's prediction of an effect or relationship.

03

Setting up the null and the alternative hypothesis

a.

Let\(\mu \)be the average full-service fee of the U.S funeral homes in the present year.

Null hypothesis:

\({H_0}:\mu = \$ 7,180\)

The average full-service fee of U.S. funeral homes in the present year is $7,180.

Alternative hypothesis:

\({H_a}:\mu < \$ 7,180\)

That is, the average full-service fee of U.S. funeral homes in the present year is less than $7,180.

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Most popular questions from this chapter

Packaging of a children’s health food. Can packaging of a healthy food product influence children’s desire to consume the product? This was the question of interest in an article published in the Journal of Consumer Behaviour (Vol. 10, 2011). A fictitious brand of a healthy food product—sliced apples—was packaged to appeal to children (a smiling cartoon apple was on the front of the package). The researchers showed the packaging to a sample of 408 school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with 1 = “not willing at all” and 5 = “very willing.” The data are summarized as follows: \(\bar x = 3.69\) , s = 2.44. Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is \(\mu = 3\).

a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use\(\alpha = 0.05\)

to make your conclusion.

b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part a? Explain.

Improving the productivity of chickens. Refer to the Applied Animal Behaviour Science (October 2000) study of the color of string preferred by pecking domestic chickens, Exercise 6.124 (p. 376). Recall that n = 72 chickens were exposed to blue string and the number of pecks each chicken took at the string over a specified time interval had a mean of\(\overline x = 1.13\,\)pecks and a standard deviation of s = 2.21 pecks. Also recall that previous research had shown that m = 7.5 pecks if chickens are exposed to white string.

a. Conduct a test (at\(\alpha = 0.01\)) to determine if the true mean number of pecks at blue string is less than\(\mu = 7.5\)pecks.
b. In Exercise 6.122, you used a 99% confidence interval as evidence that chickens are more apt to peck at white string than blue string. Do the test results, part a, support this conclusion? Explain

Accuracy of price scanners at Walmart. Refer to Exercise 6.129 (p. 377) and the study of the accuracy of checkout scanners at Walmart stores in California. Recall that the National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should have an inaccurate price. A study of random items purchased at California Walmart stores found that 8.3% had the wrong price (Tampa Tribune, Nov. 22, 2005). Assume that the study included 1,000 randomly selected items.

a. Identify the population parameter of interest in the study.

b. Set up H0 and Ha for a test to determine if the true proportion of items scanned at California Walmart stores exceeds the 2% NIST standard.

c. Find the test statistic and rejection region (at a=0.05 ) for the test.

d. Give a practical interpretation of the test.

e. What conditions are required for the inference, part d, to be valid? Are these conditions met?

Performance of stock screeners. Recall, from Exercise 6.36 (p. 350), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether \(\mu \) , the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 418.

9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1

  1. State \({H_0}\,and\,{H_a}\) for this test

Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.
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