The value of t-statistic for the following data as Population mean is 51, Sample mean is 54, Sample size is 10 and sample variance is 36,is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.5
The sample variance 36 is taken with divisor n, so the standard error is \( \frac{s}{\sqrt{n-1}} \):
\( \displaystyle \mu=51,\ \bar{x}=54,\ n=10,\ s=\sqrt{36}=6 \)
\( \displaystyle t=\frac{\bar{x}-\mu}{s/\sqrt{n-1}} \)
\( \displaystyle =\frac{54-51}{6/\sqrt{9}}=\frac{3}{2}=1.5 \)
Tip: The question gives the variance, not the standard deviation: take its square root (s = 6) before using it in the t formula; using 36 itself gives 3 ÷ 12 = 0.25.