A machine produces metal rods used in automobile suspension system. A random sample of 16 rods...

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 right-value of the confidence interval on the diameter mean?

Solutions

Expert Solution

The sample is

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

The mean is calculated as

Mean: 8.468

The sample standard deviation is calculated as

Sample standard deviation, S :

0.2538

Since the sample size is 16<30 hence we use t statistic here for the confidence interval calculation

The formula for estimation is:

μ = ± t(s_M)

where:

= sample mean
t = t statistic determined by confidence level
s = standard error = √(s²/n)

Calculation

= 8.468
t = 1.75
s = √(0.2538²/16) = 0.06

μ = ± t(s)
μ = 8.468 ± 1.75*0.06
μ = 8.468 ± 0.11123

90% CI [8.35677, 8.57923].

Now, the right-value of the confidence interval on the diameter mean is 8.57923 millimeter

orchestra answered 1 year ago

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