Answer:
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= [tex]Z_{1-\alpha /2}[/tex] * (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= [tex]Z_{1-\alpha /2}[/tex] * (δ/√n)
[tex]\frac{d}{Z_{1-\alpha /2}}[/tex]=δ/√n
√n*[tex]\frac{d}{Z_{1-\alpha /2}}[/tex]= δ
√n= δ * [tex]\frac{Z_{1-\alpha /2}}{d}[/tex]
n= ( δ * [tex]\frac{Z_{1-\alpha /2}}{d}[/tex])²
n= (45* [tex]\frac{1.96}{10}[/tex])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!
