How can I use confidence intervals for the population mean µ?
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#m+-ts#
Where #t# is the #t#-score associated with the confidence interval you require.
[ If your sample size is greater than 30 then the limits are given by
#mu # = #bar x +-(z xx SE)#]
Calculate the sample mean (#m#) and sample population (#s#) using the standard formulas.
#m=1/Nsum(x_n)#
#s=sqrt(1/(N-1)sum(x_n-m)^2#
If you assume a normally distributed population of i.i.d. (independent identically distributed variables with finite variance) with sufficient number for the central limit theorem to apply (say #N>35#) then this mean will be distributed as a #t#-distribution with #df=N-1#.
The confidence interval is then:
#m+-ts#
Where #t# is the #t#-score associated with the confidence interval you require.
If you know the population standard deviation and do not need to estimate it (#sigma#), then replace #s# with #sigma# and use a Z score from the normal distribution rather than a #t#-score since your estimate will be normally distributed rather than #t# distributed (using the above assumptions about the data).
[#barx# = sample Mean
z = critical value
SE is standard Error
SE = #sigma / sqrt(n)# Where n is sample size.
Upper limit of the population --#mu # = #bar x +(z xx SE)#
Lower limit of the population - #mu # = #bar x -(z xx SE)#
If your sample size is less than 30 use the 't' value]
