Question

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 257 students was x¯¯¯x¯ = 140 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σσ = 65 minutes in the population of all first-year students at this university.

Use the survey result to give a 95% confidence interval for the mean study time of all first-year students.

please explain your process. Thank you

Answer 1

We have given that,                              
                              
Sample mean =140                      
Population standard deviation=   65                  
Sample =257                      
Level of significance =   1-0.95=0.05                      
Z critical value (by using Z table)=1.96                  
                              
Confidence interval formula is


=(132.05,147.95)