Question

You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 80% confidence level and state that the estimated proportion must be within 1% of the population proportion. A pilot survey reveals that 8 of the 40 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements? (Round the intermediate calculations to 2 decimal places. Round the final answer to nearest whole number.) Number of persons to be interviewed

          You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 80% confidence level and state that the estimated proportion must be within 1% of the population proportion. A pilot survey reveals that 8 of the 40 sampled hold two or more jobs.
How many in the workforce should be interviewed to meet your requirements? (Round the intermediate calculations to 2 decimal places. Round the final answer to nearest whole number.)
Number of persons to be interviewed

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You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 80% confidence level and state that the estimated proportion must be within 1% of the population proportion. A pilot survey reveals that 8 of the 40 sampled hold two or more jobs.
How many in the workforce should be interviewed to meet your requirements? (Round the intermediate calculations to 2 decimal places. Round the final answer to nearest whole number.)
Number of persons to be interviewed

Added by Todd R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

10/03/2023

Step 1

We know that the confidence level is 80%, which means the level of significance (α) is 20%. Since it's a two-tailed test, we divide α by 2, so α/2 = 10%. Show more…

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You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 80% confidence level and state that the estimated proportion must be within 1% of the population proportion. A pilot survey reveals that 8 of the 40 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements? (Round the intermediate calculations to 2 decimal places. Round the final answer to nearest whole number.) Number of persons to be interviewed

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Transcript

00:01 We want to know the proportion of a workforce with two or more jobs.

00:06 But we don't know what sample size is required for the accuracy we want.

00:10 Imagine if we did know the sample size.

00:13 Well, i could take the sample, find p -hat, the sample proportion, and make a confidence interval to estimate the population proportion.

00:21 My formula would be p -hat, point estimate, plus and minus the margin of error, z root p -hat, 1 minus p -hat, over n.

00:31 I'm just going to focus on this margin of error, since we're told we should get the estimate to be within 1%.

00:37 I'm putting that in decimal form because we're going to do some calculations and percentages do not play well with calculations.

00:45 Now let's rearrange and solve for n.

00:47 Then we'll know the sample size necessary to make this true.

00:49 So we'll divide by z, square both sides, multiply by n, divide by this.

00:59 There we go.

01:00 We just need p -hat and z.

01:02 So for p -hat, we have been given a previous estimate.

01:06 A pilot survey found that 8 out of 40 met the criteria, a proportion of 0 .2.

01:14 So we're going to use that as our planning value.

01:17 We get z from the level of confidence.

01:20 Initially, this is going to be a binomial experiment.

01:23 N independent trials, two outcomes, each person either has two or more jobs or they don't...

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