Stats: Confidence Interval and Upper Limit

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A random sample of n = 18 E-glass fibre test specimens of a certain type yielded a sample average interfacial heard yield of 40 and a standard deviation of 4. Assume the interfacial shear yield stress is normally distributed. Compute the upper limit of a 95% confidence interval for the true mean stress.

Attempt: $\bar x = 40, n = 18, s=4$.

Upper limit : $$ \bar x + t_{\alpha/2,df=17}\frac{4}{\sqrt{18}} = 40 + 2.110 \times \frac{4}{\sqrt{18}} \approx 41.98932708. $$

However, the book uses $2.262$ for the $t_{\alpha/2}$ value, which seems to have df of $9$ rather than $17$ that I've used.

Did I make a mistake?

Table found @ : http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

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Seems to me you're right---for the upper end of a two-sided CI. I would round the answer to 41.99.

The wording of the problem (as edited) seems clear, but I wonder why you are asked to compute only the upper limit of a two-sided CI. If this were the upper bound for a one-sided 95% CI, you would put the full 5% in the upper tail of t(df=17) and use 1.740 instead of 2.110.

Below is the printout from Minitab statistical software, which gives both the lower and upper limits of a two-sided 95% CI.

 MTB > Onet 18 40 4.

 One-Sample T 

  N    Mean  StDev  SE Mean       95% CI
 18  40.000  4.000    0.943  (38.011, 41.989)