Question

The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.

a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.

Answer 1

b. The actual count of bike riders is too small.

d. n*p is not greater than 10.

Explanation:

Confidence interval for a proportion:

To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is,
`np \geq 10` and at least 10 failures, that is,
`n(1-p) \geq 10`

Of the 123 students surveyed 5 ride a bike to campus.

Less than 10 successes, that is:

The actual count of bike riders is too small, or
`np < 10`, and thus, options b and d are correct.