Confidence Interval of Observations Geno was trying to level across a gorge. The

Question

Confidence Interval of Observations

Geno was trying to level across a gorge. The gap from one side of the gorge to the other was rather large. This meant his foresight distance was quite long (in general not a good idea). Using an automatic level, eight foresight readings of the level rod were taken. The sample mean reading was found to be 2.3280 m. The readings had a sample standard deviation of ±3.6 mm.

a. Determine the 90% confidence interval for the eight readings (not for the population mean!). Use a precision of 0.0001 m for the confidence interval.
b. Determine whether a level reading of 2.334 m is contained in the 90% confidence interval of observations, or whether it would be considered an outlier.

Explanation / Answer

Sol:

df=n-1=8-1=7

alpha=1-0.9=0.1

alpha/2=0.1/2=0.05

t crit=1.895

90% confidence interval for the mean is

sample mean-tcrit(samplesd/sqrt(n),

sample mean+-tcrit(samplesd/sqrt(n)

2.3280 -1.895*3.6/sqrt(8),

2.3280 +1.895*3.6/sqrt(8),

-0.0839 and  4.7399

lower limit=-0.0839

upper limit=4.7399

We are 90% confident that the true population mean lies inbetween -0.0839 and 4.7399

Solutionb:
yes 2.334 m is contained in the 90% confidence interval range of 0.0839 and 4.7399

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