Question

A professor at a local community college is interested in studying the amount of hours that a college student works per week. If the professor would like to construct a 99% confidence interval for the mean hours worked per week by college students within 1.4 hours, what sample size would the professor need? A previous study found that the standard deviation for the amount of hours students work per week was 3.19 hours.

Answer 1

Solution :

Given that,

standard deviation =   =3.19

Margin of error = E = 1.4

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58

sample size = n = [Z/2* / E] 2

n = ( 2.58*3.19 / 1.4 )2

n =34.559

Sample size = n =35 rounded