Question

A machine produces metal rods used in automobile suspension system. A random sample of 16 rods is selected, and the diameter measured. The resulting data in millimeters are shown here: 8.23 8.58 8.42 8.18 8.86 8.25 8.69 8.27 8.19 8.96 8.33 8.34 8.78 8.32 8.68 8.41 Calculate a 90% confidence interval on the diameter mean. With 90% confidence, what is the left-value of the confidence interval on the diameter mean?

Answer 1

From the given data sample data,

Sample size n = 16,

Sample mean X = 8.4681
Sample standard deviation s = 0.2538

Level of confidence = 90 percent. So 1 - α = 0.90, α =0.10 and α/2 = 0.05
Therefore, t_α/2,n-1 = t_0.05,15 = 1.753

Margin of error = MOE = E =t_α/2 s/√n =1.753*0.2538/√16= 0.111
90% Confidence Interval = (X ± E) = (8.4681 ± 0.111) = (8.357, 8.579).

The 90% confidence interval on diameter mean is (8.357, 8.579).

The left – value of the confidence interval on the diameter mean is 8.357.