Confidence Intervals Examples PDF

Preview

Summary

how to calculate confidence intervals with examples...

Description

ONE SAMPLE T-INTERVAL (95% CI) USING MINITAB MTB > DATA> DATA> MTB >

set c1 2.5 3.1 2.2 1.5 2.9 end Onet C1.

One-Sample T: C1 Variable C1

N 5

Mean 2.440

StDev 0.631

SE Mean 0.282

95% CI (1.657, 3.223)

How to look up the critical t-value in Minitab (instead of using t-tables) MTB > InvCDF 0.025; SUBC> T 4. Inverse Cumulative Distribution Function Student's t distribution with 4 DF P( X > > > > > > >

# Clear the workspace rm(list=ls()) # enter the data x = c(2.5, 3.1, 2.2, 1.5, 2.9) # quick way (use built in function) t.test(x, conf.int=0.95) One Sample t-test

data: x t = 8.6484, df = 4, p-value = 0.0009833 alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: 1.656668 3.223332 sample estimates: mean of x 2.44 The long-way uses the same formulae as in class > # Long Way (step by step) > xbar = mean(x) > s=sd(x) > n=length(x) > se=s/sqrt(n) > tcrit=qt(0.025,n-1,lower.tail=F) > > me=tcrit*se > lowerbound=xbar-me > upperbound=xbar+me > > print(tcrit) [1] 2.776445 > print(lowerbound) [1] 1.656668 > print(upperbound) [1] 3.223332 > Note that the command “qt” provides for a way to get the critical values without using a table...