Suppose that a highway safety researcher is studying the design of a highway sig

Question

Suppose that a highway safety researcher is studying the design of a highway sign and is interested in the mean maximum distance at which drivers are able to read the sign. The maximum distances (in feet) at which n = 16 drivers can read the sign are as follows. 440 490 600 540 540 600 240 440 360 600 490 400 490 540 440 490

Estimate the mean maximum distance at which drivers can read the sign. If conditions are not met, make appropriate adjustments. Use a 95% confidence interval. (Outliers may be deleted in this case. Round the answers to 1 decimal place.)
feet to  feet

Explanation / Answer

Sol:

stimate the mean maximum distance at which drivers can read the sign.

mean=sum/total

= 440 +490+ 600+ 540+ 540+ 600+ 240+ 440 +360+ 600 +490+ 400+ 490+ 540+ 440 +490/16

=7700/16

mean =481.25

Use a 95% confidence interval. (Outliers may be deleted in this case. Round the answers to 1 d

outlier is

240 form boxplot

Remove 240 and find confidence inteval

sample mean=497.33

sample sd=73.43

n-1=15-1=14

alpha=0.05

alpha/2=0.05/2=0.025

t crit=2.145

95% confidence interval for true population mean=

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

497.33-2.145(73.43)/sqrt(15),497.33+2.145(73.43)/sqrt(15)

456.66,537.99

lower limit=456.66=456.7

upper limit=537.99=537.9

We are 95% confident that the true populatioin mean lies in between

456.7 and 537.9

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