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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

Question:Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a Pew Internet & American Life Project Survey (October 2010). In a representative sample of 755 adults who use the Internet, 506 admitted

that they have paid to download music. Let p represent the true proportion of all Internet-using adults who have paid to download music.

a. Compute a point estimate of p.

b. Set up the null and alternative hypotheses for testing whether the true proportion of all Internet-using adults who have paid to download music exceeds.7.

c. Compute the test statistic for part b.

d. Find the rejection region for the test if = 0.01.

e. Find the p-value for the test.

f. Make the appropriate conclusion using the rejection region.

g. Make the appropriate conclusion using the p-value.

If a hypothesis test were conducted using = 0.05, for which of the following p-values would the null hypothesis be rejected?

a. .06

b. .10

c. .01

d. .001

e. .251

f. .042

A simple random sample of 25 observations was selected from a normal population. The mean and standard deviation of this sample are 20 and 5, respectively.

a. Test H0:=22against Ha:22at the 10% significance level.

b. Test H0:22against H0:22at the 1% significance level.

鈥淪treaming鈥 of television programs is trending upward. According to The Harris Poll (August 26, 2013), over one-third of American鈥檚 qualify as 鈥渟ubscription streamers,鈥 i.e., those who watch streamed TV programs through a subscription service such as Netflix, Hulu Plus, or Amazon Prime. The poll included 2,242 adult TV viewers, of which 785 are subscription streamers. On the basis of this result, can you conclude that the true fraction of adult TV viewers who are subscription streamers differs from one-third? Carry out the test using a Type I error rate of =.10. Be sure to give the null and alternative hypotheses tested, test statistic value, rejection region or p-value, and conclusion.

A random sample of n observations is selected from a normal population to test the null hypothesis that 碌=10.Specify the rejection region for each of the following combinations of \(Ha,\alpha ,\) and n:

a.\(Ha:\)碌\( \ne 10;\alpha = .05.;n = 14\)

b.\(Ha:\)碌\( > 10;\alpha = .01;n = 24\)\(\)

c.\(Ha:\)碌\( > 10;\alpha = .10;n = 9\)

d.\(Ha:\)碌 <\(10:\alpha = .01;n = 12\)

e.\(Ha:\)碌\( \ne 10;\alpha = .10;n = 20\)

f. \(Ha:\)碌<\(10;\alpha = .05;n = 4\)

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