Question

The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the
students. How large a sample is needed if the principal would like to assert with 95% confidence that the sample mean is off by, at most, 7 minutes. Assume σ = 14 minutes. Round to the nearest whole number.

Answer 1

Solution :

Given that,

Population standard deviation = = 14

Margin of error = E = 7

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z_/2* / E) ²

n = (1.96 * 14/ 7)²

n = 15.36

n = 16

Sample size = 16