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Chapter 7: Q9E (page 398)

Americans鈥� 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鈥攚ith revenue of about $13 billion per year鈥攊s 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 鈥渢he proportion of American adults who believes professional football is their favorite sport.鈥�

The null and the alternative hypotheses are and H0 : p = 0.40 and Ha : p 鈮� 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 鈥渢he proportion of American adults who believes professional football as their favorite sport.鈥�

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 鈮� 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

Refer to Exercise 6.44 (p. 356), in which 50 consumers taste-tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below

  1. Test \({H_0}:p = .5\) against \({H_0}:p > .5\), where p is the proportion of customers who do not like the snack food. Use \(\alpha = 0.10\).
    1 0 0 1 2 0 1 1 0 0 0 1 0 2 0 2 2 0 0 1 1 0 0 0 0 1 0 2 0 0 0 1 0 0 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 1

A random sample of 64 observations produced the following summary statistics: \(\bar x = 0.323\) and \({s^2} = 0.034\).

a. Test the null hypothesis that\(\mu = 0.36\)against the alternative hypothesis that\(\mu < 0.36\)using\(\alpha = 0.10\).

b. Test the null hypothesis that \(\mu = 0.36\) against the alternative hypothesis that \(\mu \ne 0.36\) using \(\alpha = 0.10\). Interpret the result.

An analyst tested the null hypothesis that 渭 鈮� 20against the alternative hypothesis that 渭 <20. The analyst reported a p-value of .06. What is the smallest value of伪for which the null hypothesis would be rejected?

Consider the test \({H_0}:\mu = 70\) versus \({H_a}:\mu \ne 70\) using a large sample of size n = 400. Assume\(\sigma = 20\).

a. Describe the sampling distribution of\(\bar x\).

b. Find the value of the test statistic if\(\bar x = 72.5\).

c. Refer to part b. Find the p-value of the test.

d. Find the rejection region of the test for\(\alpha = 0.01\).

e. Refer to parts c and d. Use the p-value approach to

make the appropriate conclusion.

f. Repeat part e, but use the rejection region approach.

g. Do the conclusions, parts e and f, agree?

Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers鈥攖he point-spread error鈥攚as calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using 伪 = 0.10.
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