Determine the minimum sample size required to be 95% confident that the sample mean waking time is within 10 minutes of the population mean waking time. Use the population standard deviation from Exercise 1.

Step-by-step explanation:

Hello!

Text from Exercise 1:

"The waking times (in minutes past 5:00 a.m.) of 40 people who start work at 8:00 a.m. are shown in the table at the left. Assume the population standard deviation is 45 minutes."

The study variable is X: waking time (past 5:00 a.m.) of one person, measured in minutes.

Assuming the variable has a normal distribution, the margin of error, d, of the CI for the population mean waking time is:

d= * (δ/√n)

You have to calculate the sample size for a 95% CI, σ= 45min and d=10 min.

For this you have to clear the sample size from the formula:

d= * (δ/√n)

=δ/√n

√n*= δ

√n= δ *

n= ( δ * )²  

n= (45* )²

n= 77.79≅ 78

You need a sample of at least 78 people to estimate the population mean of the waking time using a 95% CI.

I hope this helps!

iu

step-by-step explanation: