Discussion
A sample of 17 measurements of the diameter of a spherical particle gave a mean = 5 μm and a standard deviation = 0.5 μm. Assuming t-statistic for 16 degrees of freedom \(t_{0.05} \approx 2\), the 95% confidence limits of actual diameter are
Answer: A
The 95 per cent confidence limits are about 4.75 and 5.25 micrometre.
The limits of the mean are the sample mean plus or minus t times the standard error, where the standard error is the standard deviation over the square root of the sample size.
\[ 5 \pm 2 \times \frac{0.5}{\sqrt{17}} = 5 \pm 0.24 \]
That gives 4.76 to 5.24, which is closest to option (A). Using the standard deviation itself (5 plus or minus 1) gives 4 to 6 micrometre, which is option (B) and is wrong, and 4.9 to 5.1 and 4.5 to 5.5 do not follow from the calculation.
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