Question

Consider a sample survey to determine the mean family income in area X. to know how many families should be sampled. In a pilot sample of 12 families, the standard deviation of the sample was Tk. 24000. Suppose you are to use the 95 percent confidence level. The estimate is to be within Tk. 1500. Estimate the number of families to be interviewed.

Answer 1

Answer: To estimate the number of families to be interviewed, we can use the formula for sample size calculation in a survey.

The formula for sample size calculation is:

n = (Z * σ / E)^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z = 1.96)

σ = standard deviation of the sample

E = desired margin of error (estimate to be within Tk. 1500)

Given information:

Pilot sample size (n) = 12

Standard deviation of the sample (σ) = Tk. 24000

Desired margin of error (E) = Tk. 1500

Substituting the values into the formula:

n = (1.96 * 24000 / 1500)^2

Calculating this:

n ≈ 31.86^2

n ≈ 1014.12

Therefore, the estimated number of families to be interviewed is approximately 1014.

Keep in mind that this is an estimate and rounding up to the nearest whole number, the recommended sample size would be 1015 families.