Question 1196763
the sample mean is equal to 8.2343
the sample standard deviation is equal to .02623
the sample size is equal to 14
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the critical t-score at 13 degrees of freedom (sample size - 1) = plus or minus 3.0123.
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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.