Question

In preparing a report on the economy, we 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 we contact in order to create an estimate in which we are 98% confident with a margin of error of 7%? b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice? c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%? a) A sample size of is needed. (Round up to the nearest whole number.)

          In preparing a report on the economy, we 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 we contact in order to create an estimate in which we are 98% confident with a margin of error of 7%?
b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice?
c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%?

a) A sample size of is needed.
(Round up to the nearest whole number.)

In preparing a report on the economy, we 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 we contact in order to create an estimate in which we are 98% confident with a margin of error of 7%?
b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice?
c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%?

a) A sample size of is needed.
(Round up to the nearest whole number.)

Added by Aaron P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Pruthvi R

03/20/2022

Step 1

However, since we don't have this information, we can use the rule of thumb that the standard deviation of a binary distribution is 0.5. The formula for the sample size is (Z-score)^2 * StdDev*(1-StdDev) / (margin of error)^2. The Z-score for a 98% confidence Show more…

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In preparing a report on the economy, we 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 we contact in order to create an estimate in which we are 98% confident with a margin of error of 7%? b) Suppose we want to reduce the margin of error to 4%. What sample size will suffice? c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%? a) A sample size of is needed. (Round up to the nearest whole number.)