confidence intervals

#1
I have a question that is driving me up the wall.

A sample of size 400 has a (sum)x = 30,430 and (sum)xsquared = 3,261,1000.
construct a 95% confidence interval for the approriate mean (mew).

I got the t-score to be 1.966 and the x avaerage to be 76.075 but when trying to do the confidence interval I don't know what to put in for s becuase i don't know how to find s (part of the studentized version) s is equal to standard deviation. does anyone know how to find this?
 

JohnM

TS Contributor
#2
There is a computational formula for the standard deviation that uses the sum of x and the sum of x^2.



Sx = Square root of {Ex2 - [(Ex)2]/n}/n-1
 

JohnM

TS Contributor
#4
I made a correction - the summation symbols didn't go in correctly.

You should get Sx = 48.7

Ex = 30,430
Ex^2 = 3,261,100
(Ex)^2 = 925,984,900

Sx = Square root of {Ex2 - [(Ex)2]/n}/n-1

= sqrt [ (3261100 - (925,984,900/400)) / 399 ]

= sqrt (946137.75 / 399)
= sqrt (2371.27)
= 48.7