Consider a random sample of 10 students having 116 cm as mean height and standard deviation as 9.798 cm. If the suggested mean height of the students population is 110 cm then the t-test statistic of the sample is: [given \(\displaystyle\frac{\sqrt{10}}{9.798} = 0.3227\)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.93
For a small sample, the one-sample t statistic is
\( \displaystyle t = \frac{\bar{x} - \mu}{s/\sqrt{n}} = (\bar{x} - \mu)\frac{\sqrt{n}}{s} \)
Here \(\bar{x} = 116\), \(\mu = 110\), n = 10 and s = 9.798 is the sample standard deviation. The given value of \(\frac{\sqrt{10}}{9.798}\) is exactly the factor \(\frac{\sqrt{n}}{s}\) in this formula:
\( \displaystyle t = (116 - 110) \times \frac{\sqrt{10}}{9.798} \)
\(= 6 \times 0.3227 = 1.936\)
The option gives this value to two decimal places as 1.93.
If 9.798 were taken as the standard deviation with divisor n, the formula would use \(\sqrt{n - 1} = 3\) instead, giving \(\frac{6 \times 3}{9.798} \approx 1.84\), which is not an option. So the question intends the form above, as its given value shows.