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Chapter 7: Q9E (page 398)

Americans’ favorite sport. The Harris Poll (December 2013) conducted an online survey of American adults to determine their favorite sport. Your friend believes professional (National Football League [NFL]) football—with revenue of about $13 billion per year—is the favorite sport for 40% of American adults. Specify the null and alternative hypotheses for testing this belief. Be sure to identify the parameter of interest.

Short Answer

Expert verified

The parameter of interest (p) is “the proportion of American adults who believes professional football is their favorite sport.”

The null and the alternative hypotheses are and H0 : p = 0.40 and Ha : p ≠ 0.40.

Step by step solution

01

Given information

As per your friend, the proportion of American adults who believe professional football is their favorite sport is 0.40.

02

Specifying the parameter of interest

Here, the parameter of interest (p) is “the proportion of American adults who believes professional football as their favorite sport.”

03

Specifying the null and the alternative hypothesis

The null and alternative hypotheses are as follows:

Null hypothesis:

H0 : p = 0.40

That is, the proportion of American adults who believes professional football is their favorite sport does not differ from 0.40.

Alternative hypothesis:

Ha : p ≠ 0.40

That is the proportion of American adults who believe professional football is their favorite sport differs from 0.40.

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Most popular questions from this chapter

Oxygen bubble velocity in a purification process. Refer to the Chemical Engineering Research and Design (March 2013) study of a method of purifying nuclear fuel waste, Exercise 6.35 (p. 349). Recall that the process involves oxidation in molten salt and tends to produce oxygen bubbles with a rising velocity. To monitor the process, the researchers collected data on bubble velocity (measured in meters per second) for a random sample of 25 photographic bubble images. These data (simulated) are reproduced in the accompanying table. When oxygen is inserted into the molten salt at a rate (called the sparging rate) of \(3.33 \times {10^{ - 6}}\) , the researchers discovered that the true mean bubble rising velocity \(\mu = .338\)

a. Conduct a test of hypothesis to determine if the true mean bubble rising velocity for the population from which the sample is selected is\(\mu = .338\)Use\(\alpha = .10\).

0.275 0.261 0.209 0.266 0.265 0.312 0.285 0.317 0.229 0.251 0.256 0.339 0.213 0.178 0.217 0.307 0.264 0.319 0.298 0.169 0.342 0.270 0.262 0.228 0.22

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.

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.

7.87 Trading skills of institutional investors. Refer to The Journal of Finance (April 2011) analysis of trading skills of institutional investors, Exercise 7.36 (p. 410). Recall that the study focused on “round-trip” trades, i.e., trades in which the same stock was both bought and sold in the same quarter. In a random sample of 200 round-trip trades made by institutional investors, the sample standard deviation of the rates of return was 8.82%. One property of a consistent performance of institutional investors is a small variance in the rates of return of round-trip trades, say, a standard deviation of less than 10%.

a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performs consistently.

b. Find the rejection region for the test using α=.05

c. Interpret the value ofαin the words of the problem.

d. A Mini tab printout of the analysis is shown (next column). Locate the test statistic andp-valueon the printout.

e. Give the appropriate conclusion in the words of the problem.

f. What assumptions about the data are required for the inference to be valid?

Complete the following statement: The smaller the p-value associated with a test of hypothesis, the stronger the support for the _____ hypothesis. Explain your answer.
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