Question

According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She decided to ask 100 architecture majors whether they had ever done an internship while at their university. She collected the responses and calculated that the proportion for her university was 43%. Which one of the following statements about the z-test is correct?

Which one of the following statements about the z-test is correct?

a. It is safe to use the z-test for p.

b. It is not safe to use the z-test for p, since n * po is not large enough.

c. It is not safe to use the z-test for p, since n * (1 − po) is not large enough.

d. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one)

Answer 1

Answer: Option 'a' is correct.

Explanation:

Since we have given that

Percentage of students in the class of 2013 has done an internship during their time as an undergraduate student = 38% = p₀

Number of architecture majors = 100

We need to check that whether students at her university had an internship rate that was higher than the national average.

Proportion for her university = 43% = p₁

Here, n = 100

Since n > 30.

so, we can use z-test.

Z-test is generally use to identify whether two means are different when the standard deviation is given.

Hence, it is safe to use the z-test for p.

Therefore, option 'a' is correct.