Question

Find the 95% confidence limits of the following data set: 202.3 g, 201.5 g, 199.3 g,...

Find the 95% confidence limits of the following data set: 202.3 g, 201.5 g, 199.3 g, 201.2 g, 197.8 g, 200.2 g, 195.6 g, and 198.7 g.

variance = 4.8507

standard deviation = 2.2024

standard error = 0.7787

Math   Statistics-And-Probability   
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Answer #1

For the below sample

202.3 , 201.5 , 199.3 , 201.2 , 197.8 , 200.2 , 195.6 , 198.7

sample mean=sum of values/total values=1596.6/8=199.575

standard deviation = 2.2024

alpha=0.05

alpha/2=0.05/2=0.025

df=n-1=8-1=7

t crit=T.INV(0.025;7)=2.36462

95% confidence interval for mean=

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

=199.575-2.36462*2.2024/sqrt(8),199.575+2.36462*2.2024/sqrt(8)

=197.7337,201.4163

lower limit=197.7337

upper limit=201.4163

we are 95% confident that the true population mean lies in between

197.7337 and 201.4163

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