A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -3.79
For a small sample, the one-sample t statistic is \(t = \frac{\bar{x} - \mu}{s/\sqrt{n}}\), where the sample variance \(s^2\) uses the divisor \(n - 1\).
Here \(n = 16\), \(\bar{x} = 53\), \(\mu = 56\) and \(\sum (x - \bar{x})^2 = 150\):
\( \displaystyle s^2 = \frac{150}{16 - 1} = 10 \)
\(s = \sqrt{10} = 3.162\)
\( \displaystyle \frac{s}{\sqrt{n}} = \frac{3.162}{4} = 0.7906 \)
\( \displaystyle t = \frac{53 - 56}{0.7906} = -3.79 \)
The other common form, \(t = \frac{\bar{x} - \mu}{S}\sqrt{n - 1}\) with \(S^2 = \frac{150}{16}\), gives the same value.