Question

Statistics Canada wants to estimate the percentage of females in the Canadian labour force to within 2% marginal error, with 90% confidence. What is the smallest sample size required for this analysis?

Answer 1

To estimate the percentage of females in the Canadian labour force to within a 2% marginal error with 90% confidence, a sample size of 1702 is required.

Step-by-step explanation:

To estimate the percentage of females in the Canadian labour force to within a 2% marginal error with 90% confidence, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

Where:

• n is the sample size
• Z is the z-score for the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)
• σ is the estimated standard deviation (we will assume a conservative value of 0.5 for the proportion of females in the population)
• E is the desired margin of error (2% = 0.02)

Plugging in these values, we get:

n = (1.645 * 0.5 / 0.02)^2 = 1701.30625

So, the smallest sample size required for this analysis is 1702 (rounded to the nearest whole number).