SOLUTION: A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are

Question 1196763: A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diameter is measured. The resulting data (in millimeters) are as follows: 8.24 8.25 8.20 8.24 8.21 8.26 8.26 8.20 8.25 8.23 8.23 8.19 8.28 8.24
The upper boundary of the 99% prediction interval on the next rod selected is?
Only the final answer should be rounded-off to TWO decimal places.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sample mean is equal to 8.2343
the sample standard deviation is equal to .02623
the sample size is equal to 14

the critical t-score at 13 degrees of freedom (sample size - 1) = plus or minus 3.0123.

to calculator the raw score, use the t-score formula of:
t = (x - m) / s
t is the t-score
x is the raw score
m is the mean
s is the standard deviation if you are looking at one value from a sample
s is the standard error if you are looking at the mean of values from a sample
standard error = standard deviation / sqrt(sample size)
for this problem, standard error = .02623 / sqrt(14) = .007
from the t-score formula, solve for x to get:
x = s * t + m
for this problem, the lower x-value becomes x = .007 * -3.0123 + 8.2343 = 8.2132 and the upper x-value becomes x = .007 * 3.0123 + 8.2343 = 8.2554
if i understand your problem correctly, the upper boundary for the next rod selected would be 8.26 and the lower boundary for the next rod selected would be 8.21.
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