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The 90% confidence interval is given by (3.9911; 7.9911)
It is 90% confident that the true average speed of a vehicle on a highway is between 3.9911 and 7.9911 miles per hour.
1) Former concept
A confidence interval is "a range of values that is likely to encompass the values of a population with some degree of confidence. Often expressed as a percentage.
The error bar is the range of values above and below the sample statistic in the confidence interval.
A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean.
X = 2, represents the sample mean of the sample
μ = population mean (variable of interest)
s = 1 represents the standard deviation of the sample
n = 11 represents the sample size
2 ) Confidence Interval:
Confidence Interval for mean is given below:
X ± t (α/2) s/√n
To compute the critical value, we first need to find the degrees of freedom given by
df = n -1
= 11 -1 = 10
Confidence is 0.90 or 90%, so the value of and is α = 0.1 , and α/2 = 0.05 you can use Excel, a calculator, or a spreadsheet to find the critical values. The Excel command would be "=-T.INV(0.05,10)".
2 - 1.81 (1/√11) = 3.9911
2 + 1.81 (1/√11) = 7.9911
So in this case the 90% confidence interval is (3.9911 , 7.9911)
We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 3.9911 and 7.9911 miles per hour.
Learn more about Confidence interval:
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