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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

“Miniature Golf with the Stars” 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 “Miniature Golf with the Stars.” 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:μ>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

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

AttitudesThe Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200 . Higher scores indicate better attitudes and study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school, on average. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

α=0.05 significance level of H0:μ=\)85,000versus Ha:μ>\(85,000, where μ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that μ=\)86,000is 0.64 Interpret this value.

How much juice? One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of 40bottles and measures the volume of liquid in each bottle.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

After once again losing a football game to the archrival, a college’s alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach. Suppose you wish to see if a majority of all living alumni is in favor of firing the coach. The appropriate standardized test statistic is

(a)z=0.64-0.50.64(0.36)100z=0.64-0.50.64(0.36)100

role="math" localid="1654432946823" (b)t=0.64-0.50.64(0.36)100t=0.64-0.50.64(0.36)100

(c)z=0.64-0.50.5(0.5)100z=0.64-0.50.5(0.5)100

(d)z=0.64-0.50.64(0.36)64z=0.64-0.50.64(0.36)64

(e)z=0.5-0.640.5(0.5)100z=0.5-0.640.5(0.5)100
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