You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 99% confidence level and a margin of error of 2%. A pilot survey reveals that 8 of the 47 sampled hold two or more jobs. (Use t Distribution Table & z Distribution Table.)How many in the workforce should be interviewed to meet your requirements? (Round z-score to 2 decimal places. Round up your answer to the next whole number.)

To determine the sample size needed for the survey, we can use the formula for the sample size of a proportion:

$n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right)$

where:

• $Z$ is the z-score corresponding to the desired confidence level,
• $p$ is the estimated proportion from the pilot survey,
• $E$ is the margin of error.

Step-by-step solution:

1. Determine the z-score for a 99% confidence level: The z-score for a 99% confidence level is approximately 2.58 (from the z Distribution Table).

2. Calculate the estimated proportion $p$ from the pilot survey: $p = \frac{8}{47} \approx 0.1702$

3. Set the margin of error $E$: $E = 0.02$

4. Plug the values into the sample size formula: $n = \left( \frac{2.58^2 \cdot 0.1702 \cdot (1 - 0.1702)}{0.02^2} \right)$

5. Calculate the sample size: $n = \left( \frac{2.58^2 \cdot 0.1702 \cdot 0.8298}{0.0004} \right)$ $n = \left( \frac{6.6564 \cdot 0.1702 \cdot 0.8298}{0.0004} \right)$ $n = \left( \frac{0.9395}{0.0004} \right)$ $n = 2348.75$

6. Round up to the next whole number: $n \approx 2349$

Therefore, to meet the requirements of the survey, you should interview 2349 individuals in the workforce.

To calculate the sample size needed for the survey, we will use the formula for sample size in proportion:

n = (Z^2 * P * (1-P)) / E^2

where:

• n is the sample size
• Z is the z-score corresponding to the desired confidence level
• P is the estimated proportion of the population
• E is the desired margin of error

Step 1: Find the Z-score For a 99% confidence level, the Z-score is approximately 2.57 (from the Z distribution table).

Step 2: Calculate the estimated proportion (P) From the pilot survey, we found that 8 out of 47 people hold two or more jobs. So, P = 8/47 = 0.1702.

Step 3: Calculate the margin of error (E) The desired margin of error is 2%, or 0.02.

Step 4: Substitute the values into the formula and solve for n:

n = (2.57^2 * 0.1702 * (1-0.1702)) / 0.02^2 n = 2191.67

Since we can't interview a fraction of a person, we round up to the next whole number. Therefore, you should interview approximately 2192 people in the workforce to meet your requirements.