20. Jorge conducted a survey by asking 120 students whether they use a pencil to take notes. Of the students surveyed, 90 responded favorably. Which margin of error matches each confidence level for this situation? 1. 90% =
2. 99% =
3. 95%=
options- 0.102, 0.338, 0.216, 0.077, 0.256, 0.065

Margin of error for 90% C.I: 0.065

Margin of error for 99% C.I: 0.091

Margin of error for 95% C.I: 0.077

Step-by-step explanation:

In this question, for each student, there are only two possible outcomes. Either they use a pencil to take notes, or they do not. Students are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial confidence interval:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

For this problem, we have that:

120 students, so

90 responded favorably, so

Margin of error for 90% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is:

Margin of error for 99% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is:

Margin of error for 95% CI:

Here , z is the value of Z that has a pvalue of , so .

The margin of error is: