Question

An educational professional wants to determine the number of times students procrastinate on doing homework each week. They designed a chart for students to log their data. Find number of students that will be needed​ (the sample​ size) in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 2 times.​ (The professional estimated the standard deviation to be 3.25 which was found from an earlier​ study.)

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 3.25

Margin of error = E = 2

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

sample size = n = (Z_$\alpha$/2* $\sigma$ / E) ²

n = (1.645 * 3.25/ 2)²

n = 7.15

n = 8

Sample size = 8