Question

false a cooking school believes that 74% of applicants to that school have parents who were alumni. how large a sample is needed to estimate the true proportion of students who have parents who were alumni to within 0.05 with 95% confidence?

Answer 1

To estimate the true proportion of students with alumni parents within a 0.05 margin of error and 95% confidence, a sample size of approximately 295 is needed.

Step-by-step explanation:

To estimate the true proportion of students who have parents that are alumni to within 0.05 with 95% confidence, we can use the formula for the sample size of a proportion:

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

Where:

• n is the sample size
• Z is the Z-value corresponding to the desired confidence level (1.96 for 95% confidence)
• p is the estimated proportion (0.74 in this case)
• E is the desired margin of error (0.05)

Plugging the values into the formula, we have:

n = (1.96^2 * 0.74 * (1 - 0.74)) / 0.05^2

n = (3.8416 * 0.74 * 0.26) / 0.0025

n = 0.73575296 / 0.0025

n ≈ 294.301

Since we cannot survey a fraction of a person, we always round up to the nearest whole number when determining sample size. Therefore, the sample size needed is approximately 295.