A sociologist develops a test to measure attitudes about public transportation.She wishes to compute a 95% confidence interval for the mean score on this test.It is believed that the standard deviation for these test scores will be 21.How many people should be given the test in order to achieve a margin of error of 10?

Question

Quizplus · Accepted Answer

The margin of error, E, is given by:
E = z(α/2) * (σ/√n)
where z(α/2) is the z-score corresponding to the level of confidence α/2, σ is the standard deviation, and n is the sample size.

We want E = 10, α = 0.05 (for a 95% confidence interval), and σ = 21.
So we have:
10 = z(0.025) * (21/√n)
Using a z-table or calculator, we find that z(0.025) ≈ 1.96.
Plugging in the values, we get:
10 = 1.96 * (21/√n)
Solving for n, we get:
n ≈ 20.17
Since we can't have a fractional number of people, we round up to the nearest integer: n = 20.
Therefore, the answer is B.

A Sociologist Develops a Test to Measure Attitudes About Public