Question 1

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 39 students who took the survey, 25 were judged to have a visual learning style and 14 were considered verbal learners.
-Determine a $90 \%$ confidence interval for the population proportion who are visual learners at this university.

Accepted Answer

A $90 \%$ confidence interval for the population proportion who are visual learners at this university is

Question 2

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 39 students who took the survey, 25 were judged to have a visual learning style and 14 were considered verbal learners.
-Write a sentence interpreting what this interval says.

Accepted Answer

You are $90 \%$ confident the population proportion of visual learners at this university is between $51.5 \%$ and $76.7 \%$.

Question 3

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 39 students who took the survey, 25 were judged to have a visual learning style and 14 were considered verbal learners.
-How would a $99 \%$ confidence interval compare to this one in terms of its midpoint and half-width? (Do not bother to determine this interval.)

Accepted Answer

A $99 \%$ confidence interval would have the same midpoint (.641) as the $90 \%$ confidence interval, but it would have a larger half-width because the $z^{*}$ value used to create the $99 \%$ interval would be greater than 1.645 .

Question 4

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 39 students who took the survey, 25 were judged to have a visual learning style and 14 were considered verbal learners.
-Check whether the technical condition concerning sample size is satisfied here.

Accepted Answer

The answer of Students enrolled in an introductory statistics course...

Question 5

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 39 students who took the survey, 25 were judged to have a visual learning style and 14 were considered verbal learners.
-Explain why you might feel wary about applying this confidence interval to the population of all students at this university.

Accepted Answer

The answer of Students enrolled in an introductory statistics course...

Question 6

You have learned that a confidence interval for $\pi$ is given by: $\hat{p} \pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.
-What does the symbol $\pi$ stand for?

Accepted Answer