Question

A class survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" There were 464 responses to the class survey. Suppose that we know that the study time follows a Normal distribution with standard deviation

σ = 8.6

hours in the population of all first-year students at this university.

One student claimed to study 10,000 hours per week (10,000 is more than the number of hours in a year). We know he's joking, so we would leave out this value. If we did a calculation without looking at the data, we would get

x = 36.3

hours for all 464 students. What is the 99% confidence interval for the population mean? (Round your answers to two decimal places.)

______ to _____ Hours

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 36.3

Population standard deviation =    = 8.6

Sample size = n = 464

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 * ( 8.6 /  464 )

= 0.40

At 99% confidence interval estimate of the population mean is,

  ± E

36.3 ± 0.40   

35.90 to ,36.70 Hours