To prepare a report on the economy, analysts need to estimate the percentage of

Question

To prepare a report on the economy, analysts need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. (a) How many randomly selected employers must you contact in order to guarantee a margin of error no more than 15% (at 95% confidence)? (b) If analysts believe that at most 20% of firms are likely to be hiring, how many must they survey to obtain a margin of error of 0.15? (a) The company needs to contact randomly selected employers. (b) The company needs to survey randomly selected firms.

Explanation / Answer

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.15
n = ( 1.96 / 0.15 )^2 * 0.5*0.5
= 42.684 ~ 43
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.2
ME = 0.15
n = ( 1.96 / 0.15 )^2 * 0.2*0.8
= 27.318 ~ 28

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