Question

Sleep – College Students: Suppose you perform a study about the hours of sleep that college students get. You know that for all people, the average is 7.0 hours with a standard deviation of 1.3 hours. You randomly select 50 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.40 hours. Assume the population standard deviation for college students is the same as for all people. We want to construct a 95% confidence interval for the mean number of hours of sleep for all college students.

(a) What is the point estimate for the mean amount of sleep for all college students?
  hours

(b) What is the critical value of z (denoted z_α/2) for a 95% confidence interval? Use the value from the table or, if using software, round to 2 decimal places.
z_α/2 =

(c) What is the margin of error (E) for the mean number of hours of sleep for all college students for a 95% confidence interval? Round your answer to 3 decimal places.
E =  hours

(d) Construct the 95% confidence interval for the mean number of hours of sleep for all college students. Round your answers to 2 decimal places.
  < μ <  

Answer 1

Solution :

Given that,

a) Point estimate = sample mean = = 6.40

Population standard deviation =    = 1.3

Sample size = n =50

b) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

c) Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 1.3 /  50 )

= 0.360

d) At 95% confidence interval estimate of the population mean is,

- E < < + E

6.40 - 0.360 <   < 6.40 + 0.360

( 6.04 <   < 6.76 )