Question

In: Statistics and Probability

For each situation described​ below, identify the population and the​ sample, explain what p and p...

For each situation described​ below, identify the population and the​ sample, explain what p and p with modifying above ​represent, and tell whether it is appropriate to create a​ one-proportion z-interval. Complete parts a through d below.

a) Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems. They find that 25 of the 139

cars stopped have at least one safety violation. They want to estimate the percentage of all cars that may be unsafe.

Identify the population. Choose the correct answer below.

A. The passengers of those cars actually stopped at the checkpoint

B. All cars

C. All car passengers

D. Those cars actually stopped at the checkpoint

Identify the sample. Choose the correct answer below.

A. Those cars actually stopped at the checkpoint

B. All cars

C. All car passengers

D. The passengers of those cars actually stopped at the checkpoint

What does p represent?

A. The proportion of all cars with safety problems

B. The proportion of cars actually seen with safety problems

C. The sample size

D.The standard deviation of the proportion of cars actually seen with safety problems

What does p with modifying above represent?

A. The sample size

B. The standard deviation of the proportion of cars actually seen with safety problems

C. The proportion of cars actually seen with safety problems

D. The proportion of all cars with safety problems

Is it appropriate to create a one-proportion z-interval?

A. It is not appropriate because the sample is a simple random sample.

B. It is not appropriate because the sample is less than​ 10% of the population.

C. If the sample left parenthesis a cluster sample right parenthesis is representative comma then it is appropriate to create aIf the sample (a cluster sample) is representative, then it is appropriate to create a one dash proportion z dash interval.one-proportion z-interval.

D. It is appropriate because the sample is less than​ 10% of the population.

b) An online blog puts a poll on its website asking readers to rate the quality of its articles. Of the 568 people who voted, 395 rated the articles very highly. The blog is interested in gauging its users' satisfaction.

Identify the population. Choose the correct answer below.

A. Those who voted in the poll

B. All U.S. voters

C. Internet users

D. The blog's readers

Identify the sample. Choose the correct answer below.

A. Internet users

B. The blog's readers

C. All U.S. voters

D. Those who voted in the poll

What does p represent?

A. The proportion of people who use the internet

B. The proportion of those who voted in the poll who rated the articles very highly

C. The proportion of all the blog's readers who rate its articles very highly

D. The probability of a​ "failure"

What does p with modifying above represent?

A. The proportion of people who use the internet

B. The proportion of those who voted in the poll who rated the articles very highly

C. The probability of a​ "failure"

D. The proportion of all the blog's readers who rate its articles very highly

Is it appropriate to create a one-proportion z-interval?

A. If the sample​ (cluster sample) is​ representative, then it is appropriate to create a​ one-proportion z-interval.

B. It is appropriate because the sample is less than​ 10% of the population.

C. It is not appropriate because the sample is biased and nonrandom.

D. It is not appropriate because there not at least 10​ "successes" and 10​ "failures."

c) A school is considering requiring students to wear uniforms. The PTA surveys parent opinion by sending a questionnaire home with 1118 students. 485 surveys are returned, with 104 in favor of the change.

Identify the population. Choose the correct answer below.

A. The 1118 people who received questionnaires.

B. The U.S. population

C. The parents of students at the school

D. Those who returned the questionnaire

Identify the sample. Choose the correct answer below.

A. The U.S. population

B. The 1118 people who received questionnaires

C. The parents of students at the school

D. Those who returned the questionnaire

What does p represent?

A. The proportion of all parents who favor uniforms

B. The proportion of questionnaires returned

C. The proportion of parents of students at the school who favor the change

D. The proportion of respondents who favor uniforms

What does p with modifying above represent?

A. The proportion of respondents who favor uniforms

B. The proportion of all parents who favor uniforms

C. The proportion of parents of students at the school who favor the change

D. The proportion of questionnaires returned.

Is it appropriate to create a one-proportion z-interval?

A. If the sample​ (simple random​ sample) is​ representative, then it is appropriate to create a​ one-proportion z-interval.

B. It is not appropriate because there not at least 10​ "successes" and 10​ "failures."

C. It is not appropriate because the​ respondents' answers are independent.

D. It is not appropriate because this is not a simple random sample and there is a possible nonresponse bias.

​d) A college admits 1743 freshmen one​ year, and four years​ later, 1502 of them graduate on time. The college wants to estimate the percentage of all their freshman enrollees who graduate on time.

Identify the population. Choose the correct answer below.

A. The 1502 students who graduated on time

B. Students at the college

C. All college students

D. The 1743 students who entered that year

Identify the sample. Choose the correct answer below.

A. The 1743 students who entered that year

B. The 1502 students who graduated on time

C. All college students

D. Students at the college

What does p represent?

A. The proportion of all students at the college who will not graduate on time

B. The proportion of students at the college who are freshmen

C. The proportion of all students at the college who will graduate on time

D. The proportion of that​ year's students who will graduate on time

What does p with modifying above represent?

A. The proportion of students at the college who are freshmen

B. The proportion of that​ year's students who will graduate on time

C. The proportion of all students at the college who will not graduate on time

D. The proportion of all students at the college who will graduate on time

Is it appropriate to create a one-proportion z-interval?

A. It is not appropriate because the sample is a simple random sample.

B. It is not appropriate because this is not a simple random sample and there is a possible nonresponse bias.

C. It is not appropriate because whether a student graduates on time is independent of whether another student graduates on time.

D. If that​ year's students​ (a cluster​ sample) are viewed as a representative sample of all possible students at the​ school, then it is appropriate to create a​ one-proportion z-interval.

Solutions

Expert Solution

a) Police set up an auto checkpoint at which drivers are stopped and their cars inspected for safety problems. They find that 25 of the 139 cars stopped have at least one safety violation. They want to estimate the percentage of all cars that may be unsafe.

Identify the population. Choose the correct answer below.

B. All cars

Identify the sample. Choose the correct answer below.

A. Those cars actually stopped at the checkpoint

What does p represent?

A. The proportion of all cars with safety problems

What does p with modifying above represent?

C. The proportion of cars actually seen with safety problems

Is it appropriate to create a one-proportion z-interval?

C. If the sample left parenthesis a cluster sample right parenthesis is representative comma then it is appropriate to create aIf the sample (a cluster sample) is representative, then it is appropriate to create a one dash proportion z dash interval.one-proportion z-interval.

b) An online blog puts a poll on its website asking readers to rate the quality of its articles. Of the 568 people who voted, 395 rated the articles very highly. The blog is interested in gauging its users' satisfaction.

Identify the population. Choose the correct answer below.

D. The blog's readers

Identify the sample. Choose the correct answer below.

D. Those who voted in the poll

What does p represent?

C. The proportion of all the blog's readers who rate its articles very highly

What does p with modifying above represent?

B. The proportion of those who voted in the poll who rated the articles very highly

Is it appropriate to create a one-proportion z-interval?

A. If the sample​ (cluster sample) is​ representative, then it is appropriate to create a​ one-proportion z-interval.

c) A school is considering requiring students to wear uniforms. The PTA surveys parent opinion by sending a questionnaire home with 1118 students. 485 surveys are returned, with 104 in favor of the change.

Identify the population. Choose the correct answer below.

C. The parents of students at the school

Identify the sample. Choose the correct answer below.

B. The 1118 people who received questionnaires

What does p represent?

A. The proportion of all parents who favor uniforms

What does p with modifying above represent?

A. The proportion of respondents who favor uniforms

Is it appropriate to create a one-proportion z-interval?

D. It is not appropriate because this is not a simple random sample and there is a possible nonresponse bias.

​d) A college admits 1743 freshmen one​ year, and four years​later, 1502 of them graduate on time. The college wants to estimate the percentage of all their freshman enrollees who graduate on time.

Identify the population. Choose the correct answer below.

D. The 1743 students who entered that year

Identify the sample. Choose the correct answer below.

B. The 1502 students who graduated on time

What does p represent?

B. The proportion of students at the college who are freshmen

What does p with modifying above represent?

B. The proportion of that​ year's students who will graduate on time

Is it appropriate to create a one-proportion z-interval?

B. It is not appropriate because this is not a simple random sample and there is a possible nonresponse bias.

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orchestra answered 2 years ago
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