Question

The population standard deviation for the age of Foothill College students is 15 years. If we want to be 95% confident that the sample mean age is within 2 years of the true population mean age of Foothill College students , how many randomly selected Foothill College students must be surveyed?
From the problem, we know that σ = 15 and EBM = 2
z = z.025 = 1.96, becuase the confidence level is 95%.
n=\frac{z^{^{2}}\sigma ^{2}}{EBM^{2}}=\frac{1.96^{^{2}}15 ^{2}}{2^{2}}=216.09
using the sample size equation.
Use n = 217: Always round the answer UP to the next higher integer to ensure that the sample size is large enough.
Therefore, 217 Foothill College students should be surveyed in order to be 95% confident that we are within 2 years of the true population mean age of Foothill College students.

Answer 1

At 95% confidence, z is 1.96

and given that Population standard deviation = 15

E = 2

Thus

Number of Foothill College students required for survey

n= (1.96 x15/2)²

n = 216.09