Question

An independent random sample is selected from an approximately normal population with an unknown standard deviation. a) Given the sample mean = 24.3, sample standard deviation = 8.5, and sample size = 32, compute the standard error. The standard error = b) Using a confidence coefficient of 2.04, compute the confidence interval. The 95% confidence interval goes from to (Enter the smaller number first.) c) Based on the confidence interval above, which of the following values are plausible? (Choose all answers that are plausible.) 10 12 15 18 24 27 30 45

Answer 1

a) Standard Error , SE = s/√n =   8.5/√32=   1.5026

b)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   31          
't value='   tα/2=   2.040   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   8.5/√32=   1.5026          
margin of error , E=t*SE =   2.0400   *   1.5026   =   3.0653
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    24.30   -   3.0653   =   21.234692
Interval Upper Limit = x̅ + E =    24.30   -   3.0653   =   27.365308
95%   confidence interval is (   21.23   < µ <   27.37   )

c) answer: 24,27