Question

A survey of 250 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 115 of the 250 students responded​ "yes." An approximate 95​% confidence interval is (0.397​,0.523​). Which of the following are​ true? If they are not​ true, briefly explain why not

a)95​% of the students fall in the interval ​(0.397​,0.523​).

​b) The true proportion of students who use laptops to take notes is captured in the interval left parenthesis 0.397 comma 0.523 right parenthesis with probability 0.95.

​c) There is a 46​% chance that a student uses a laptop to take notes.

​d) There is a 95​% chance that the student uses a laptop to take notes 46​% of the time.

​e) We are 95​% confident that the true proportion of students who use laptops to take notes is captured in the interval left parenthesis 0.397 comma 0.523 right parenthesis.

a) Choose the correct answer below.

A. The statement is false. 46​% of the students fall in the interval ​(0.397​,0.523​).

B. The statement is false. This​ doesn't make sense because students are not proportions.

C. The statement is true.

D. The statement is false. The sample size is too small to make this claim.

​b) Choose the correct answer below.

A. The statement is false. The population proportion is either within the interval or not within the interval.

B. The statement is true.

C. The statement is false. The sample size is too small to make this claim.

D. The statement is false. We are 46​% confident that the sample proportion of students who use a laptop to take notes is between 39.7​% and 52.3​%. ​

c) Choose the correct answer below.

A. The statement is false. There is not enough information to make an absolute statement about the population value with precision.

B. The statement is true.

C. The statement is false. There is a​ 5% chance that a random selected student uses a laptop to take notes.

D. The statement is false. The sample size is too small to make this claim.

​d) Choose the correct answer below.

A. The statement is false. There is a 54​% chance that a random selected coworker uses a laptop to take notes.

B. The statement is true.

C. The statement is false. The sample size is too small to make this claim.

D. The statement is false. This​ doesn't make sense because​ it's not about the proportion of the time that a student uses a laptop. ​

e) Choose the correct answer below.

A. The statement is false. We are 46​% confident that between 39.7​% and 52.3​% of the samples will have a proportion near 95​%.

B. The statement is false. The sample size is too small to make this claim.

C. The statement is false. The statement should be about the true​ proportion, not future samples.

D. The statement is true.

Answer 1

a)95​% of the students fall in the interval ​(0.397​,0.523​).

B. The statement is false. This​ doesn't make sense because students are not proportions.

b) The true proportion of students who use laptops to take notes is captured in the interval left parenthesis 0.397 comma 0.523 right parenthesis with probability 0.95.

  A. The statement is false. The population proportion is either within the interval or not within the interval.

c) There is a 46​% chance that a student uses a laptop to take notes.

A. The statement is false. There is not enough information to make an absolute statement about the population value with precision.

​d) There is a 95​% chance that the student uses a laptop to take notes 46​% of the time.

  D. The statement is false. This​ doesn't make sense because​ it's not about the proportion of the time that a student uses a laptop. ​

​e) We are 95​% confident that the true proportion of students who use laptops to take notes is captured in the interval left parenthesis 0.397 comma 0.523 right parenthesis.

  D. The statement is true.