Tuesday, January 27, 2009

Excel: Confidence interval

You can use both t and z distribution to create confidence interval around sample mean. You use t when the sample size is less than 30 (n<30).

Hence with 0.05 (95%) level of confidence our interval is: mean±interval i.e. 182.4±20.719 and 45±4.6924, respectively.
For illustration only there is also z statistic interval shown (19.4 and 4.39 respectively). As can be seen, using z instead of t makes the interval to be smaller.

If one wants to use for example, 0.01 (99%) level of confidence one must use TINV(0.01,n-1) for t distribution and CONFIDENCE(0.01,STDEV,n) for z distribution.
In our case if we use 0.01 we get interval for t distribution equal to 28.3207 for the first example and 6.4141 for the second example. Interval for z is 25.50 and 5.77 respectively.

Briefly:Interval using z distribution is narrower
than for t distribution

The same but in R:
>X1 <- scan()
1: 205 179 185 210 128 145 177 117 221 159 205 128 165 180 198 158 132 283 269 204
> a <- mean(X1)
> s <- sd(X1)
> n <- length(X1)
> errZ <- qnorm(0.975)*s/sqrt(n)
> errT <- qt(0.975,df=n-1)*s/sqrt(n)


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