91影视

How much juice? Refer to Exercises 3 and 11 .

a. What conclusion would you make at the $伪=0.10伪=0.10$level?

b. Would your conclusion from part (a) change if a 5 \% significance level was used instead? Explain your reasoning.

Don鈥檛 argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the $伪=0.01$ level?

b. Would your conclusion from part (a) change if a $5\%$ significance level was used

instead? Explain your reasoning.

Making conclusions A student performs a test of $H_0:p=0.75$versus $H_a:p<0.75$at $伪=0.05$significance level and gets a $P$-value of $0.22$

The student writes: 鈥淏ecause the P-value is large, we accept $H_0$. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Don't argue! A Gallup poll report revealed that $72\%$of teens said they seldom or never argue with their friends. $3$Yvonne wonders whether this result holds true in her large high school, so she surveys a random sample of $150$students at her school.

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

Making conclusions A student performs a test of $H_0:渭=12$versus $H_a:渭鈮�12$

at the $伪=0.05$significance level and gets a $P$-value of $0.01$. The

student writes: 鈥淏ecause the $P$-value is small, we reject $H_0$. The data prove that $H_a$is true.鈥� Explain what is wrong with this conclusion.

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be $1$pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is $0.975$pound.

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

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is $0.0806$. Interpret the P-value.

d. What conclusion would you make at the $伪=0.01$ significance level?

Philly fanatics? Nationally, the proportion of red cars on the road is $0.12.$A statistically minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes a random sample of $210$cars parked at Citizens Bank Park (the Phillies home field), and counts $35$red cars.

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

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in (a) is 0.0187. Interpret the P-value.

d. What conclusion would you make at the 伪=0.05 significance level?

Opening a restaurant You are thinking about opening a restaurant and are

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

$H_0:渭=\backslash )85,000$

$H_a:渭>\$85,000$

where $渭$is the true mean income in the population of people who live near the restaurant. Describe a Type $I$ error and a Type $II$ error in this setting, and give a possible consequence of each.

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 $2000$U.S. adults if they watch 鈥淢iniature Golf with the Stars.鈥� The network uses the data to perform a test of

$H_0:p=0.12$

$H_a:p>0.12$

where $p$is the true proportion of all U.S. adults who watch the show. Describe a Type $I$error and a Type$II$error in this setting, and give a possible consequence of each.

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within $8$minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than $8$minutes to arrive on $22\%$of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After $6$months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the $伪=0.05$level of $H_0$: $p=0.22$versus $H_a:p<0.22$, where $p$is the true proportion of calls involving life-threatening injuries during this $6$-month period for which emergency personnel took more than $8$minutes to arrive.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the manager鈥檚 choice of $伪=0.05$? Why or why not?