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Chapter 9: Q 24. (page 565)

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

鈥淢iniature Golf with the Stars鈥� will only be renewed if it can be established that more than 12%of U.S. adults watch the show. A polling company asks a random sample of 2000U.S. adults if they watch 鈥淢iniature Golf with the Stars.鈥� The network uses the data to perform a test of

H0:p=0.12

Ha:p>0.12

where pis the true proportion of all U.S. adults who watch the show. Describe a Type Ierror and a TypeIIerror in this setting, and give a possible consequence of each.

Short Answer

Expert verified

Type Ierror rejects null hypothesis H0, once H0is true.

Type IIerror fails to reject null hypothesis H0, once H0is false.

Step by step solution

01

Given Information

It is given that n=2000

H0:p=0.12

H1:渭>0.12

02

Explanation

Once null hypothesis H0is true, type I error is rejecting it.

Convincing evidence is present that US adults watching show is >0.12if true proportion of US adults who watch show is actually 0.12

Another consequence is that renewing the show, not sufficient people watch the show will led to loss by television network.

Once H0is false, type II error fails to reject H0.

No convincing evidence is present that true proportion of US adults watching show is >0.12, if true proportion of US adults who watch show is actually over 0.12.

Another consequence is that not renewing the show, sufficient people watch the show will led to missing a chance to make profit by television network.

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Most popular questions from this chapter

Walking to school A recent report claimed that 13%of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13at her large elementary school. She surveys a random sample of 100students and finds that 17typically walk to school. DeAnna would like to carry out a test at the 伪=0.05significance level of H0:p=0.13versus Ha:p>0.13, where p= the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

A significance test allows you to reject a null hypothesis H0H0in favor of an alternative hypothesisHaaat the 5%significance level. What can you say about significance at the1%level?

a.H0H0can be rejected at the1%significance level.

b. There is insufficient evidence to rejectH0H0at the1%significance level.

c. There is sufficient evidence to accept H0H0at the 1%significance level.

d.HaHacan be rejected at the 1%significance level.

e. The answer can't be determined from the information given.

Fast connection? How long does it take for a chunk of information to travel

from one server to another and back on the Internet? According to the site

internettrafficreport.com, the average response time is 200 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect data on response times (in milliseconds) for a random sample of 14 servers in Europe. A graph of the data reveals no strong skewness or outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 95% confidence interval for the mean response time is 158.22 to 189.64

milliseconds. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 5% significance level?

d. Do we have convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds? Justify your answer.

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either 伪=0.05or 伪=0.01

b. significant at 伪=0.05but not at伪=0.01

c. significant at伪=0.01but not at 伪=0.05

d. significant at both 伪=0.05and伪=0.01

e. inconclusive because we don鈥檛 know the value of p^
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