Question

In: Statistics and Probability

Last year, 30% of high school students in a particular county were able to find a...

  1. Last year, 30% of high school students in a particular county were able to find a summer job. A county official wants to estimate this quantity again this year. She wants to be 95% confident that the margin of error is no larger than 2%. Find the smallest sample size that would allow the official to achieve her goals.

    a.

    21
    b.

    2017
    c.

    10
    d.

    474

Solutions

Expert Solution

Solution :

Given that,

= 0.30

1 - = 1 - 0.30 = 0.70

margin of error = E =2% = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.02)2 * 0.30 * 0.70

= 2017

orchestra answered 2 years ago
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