Question

In a survey, the planning value for the population proportion is p* = 0.25. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.07? (Round your answer up to nearest whole number.)

Answer 1

To provide a 95% confidence interval with a margin of error of 0.07 when the population proportion is 0.25, the minimum sample size needed is 148, after applying the sample size formula and rounding up to the nearest whole number.

Step-by-step explanation:

To determine how large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.07, when the planning value for the population proportion is p* = 0.25, we use the formula for sample size for proportions which is:

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

Where:

• Z is the Z-value from the standard normal distribution for a 95% confidence level, which is 1.96.
• p is the estimated population proportion, in this case, p = 0.25.
• E is the margin of error, which is 0.07.

Substituting the values in, we get:

n = (1.96^2 * 0.25 * (1-0.25)) / 0.07^2

n = (3.8416 * 0.25 * 0.75) / 0.0049

n = (0.7218) / 0.0049

n ≈ 147.3061

Since we always round up to the nearest whole number when determining sample size, the minimum sample size you would need is 148.