A random sample of 16 bottles gives a mean volume of 82 ml, while the test value is 80 ml. If the value of the one-sample t-statistic is 1.6, the sample standard deviation s (calculated with divisor n − 1) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5 ml
The t-statistic is the difference of the means divided by the standard error:
\( \displaystyle t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} \)
\( \displaystyle 1.6 = \frac{82 - 80}{s/4} \)
So the standard error is
\( \displaystyle \frac{s}{4} = \frac{2}{1.6} = 1.25 \)
\( s = 4 \times 1.25 = 5 \)
Why the other options are incorrect
Option (1) 1.25 ml — Incorrect. 1.25 is the standard error \(s/\sqrt{n}\), not s itself.
Option (2) 20 ml — Incorrect. This is 1.25 × 16, multiplying by n instead of by \(\sqrt{n} = 4\).
Option (3) 0.8 ml — Incorrect. This is 1.6 ÷ 2, the ratio turned upside down.