Question

The scientific productivity of major world cities was the subject of a recent study. The study determined the number of scientific papers published between 1994 and 1997 by researchers from each of the 20 world cities, and is shown below.

City	Number of papers	City	Number of papers
City 1	66	City 11	1717
City 2	1919	City 12	1616
City 3	2525	City 13	1717
City 4	2424	City 14	66
City 5	1818	City 15	2626
City 6	2727	City 16	2222
City 7	77	City 17	1717
City 8	2525	City 18	99
City 9	2323	City 19	55
City 10	1313	City 20	6

Construct a 99 % confidence interval for the average number of papers published in major world cities.

<μ<

Answer 1

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   7.6254
Sample Size ,   n =    20
Sample Mean,    x̅ = ΣX/n =    16.4000

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   19          
't value='   tα/2=   2.8609   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   7.6254   / √   20   =   1.7051
margin of error , E=t*SE =   2.8609   *   1.7051   =   4.8782
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    16.40   -   4.878182   =   11.5218
Interval Upper Limit = x̅ + E =    16.40   -   4.878182   =   21.2782
99%   confidence interval is (   11.522   < µ <   21.278   )