Question

q1) The 95% confidence interval for the mean, calculated from a sample is 1.412011 ≤ μ ≤ 2.587989. Determine the sample mean X^-(this one x dash) =   

q2) Assuming that the data is normally distributed with the population standard deviation =1.5, determine the size of the sample n =

Answer 1

confidence interval is                  
lower limit =    1.412011              
upper limit=   2.587989              
sample mean = (lower limit+upper limit)/2= (   1.412011   +   2.587989   ) / 2 =   2

2)

margin of error = (upper limit-lower limit)/2= (   2.587989   -   1.412011   ) / 2 =   0.587989
alpha =   1-CL =   5%                  
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]              
                          
Sample Size,n = (Z * σ / E )² = (   1.960   *   1.5   /   0.587989   ) ² =   25.000
                          
                          
So,Sample Size needed=       25