Question

5. Past experience shows that the standard deviation of the distances traveled by consumers to patronize Chinese restaurants is 2 km. How large a sample is needed to estimate the population mean distance traveled to within 0.4 km

Answer 1

96

Explanation:

Given that :

Standard deviation (s) = 2km

Error in estimation is within 0.4 km ; Error (E) = 0.4 km

Using the relation :

Sample size = ((Zα/2 * s) /E)^2

Using α = 0.05

The Zcritical at 0.05 = Z0.025 = 1.96

Sample size = ((1.96 * 2) / 0.4)^2

Sample size = (3.92 / 0.4)^2

Sample size = 9.8²

Sample size = 96.04

Required sample size = 96