Question

The population standard deviation for the age of Foothill College students is 15 years. If we want to be 90% 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?

Answer 1

To be 90% confident that the sample mean age is within 2 years of the true population mean age, 217 Foothill College students must be surveyed.

Step-by-step explanation:

In order to determine how many randomly selected Foothill College students must be surveyed to be 90% confident that the sample mean age is within 2 years of the true population mean age, we can use the formula for the confidence interval:

sample mean ± (critical value) × (population standard deviation) / √(sample size)

Since the critical value for a 90% confidence level is approximately 1.645, we can plug in the given values to find the sample size:

2 = 1.645 × 15 / √(sample size)

Solving for the sample size, we get:

sqrt(sample size) = 1.645 × 15 / 2

sample size = (1.645 × 15 / 2)^2 = 217