The average rainfall in a given hilly area is 14 mm. A local weather department observes the rainfall in a part of a year as per the data given below:
| Month | May | June | July | Aug | Sept |
| Rainfall (in mm) | 14 | 12 | 18 | 16 | 20 |
Then the value of t-test statistic is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.414
This is a one-sample t-test of the sample mean against the population mean \( \mu=14 \), with n = 5.
\( \displaystyle \bar{x}=\frac{14+12+18+16+20}{5}=\frac{80}{5}=16 \)
Deviations from the mean: −2, −4, 2, 0, 4.
\( \displaystyle \sum(x-\bar{x})^2=4+16+4+0+16=40 \)
The sample standard deviation (with divisor n − 1) is
\( \displaystyle s=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}=\sqrt{\frac{40}{4}}=\sqrt{10} \)
\( \displaystyle t=\frac{\bar{x}-\mu}{s/\sqrt{n}} \)
\( \displaystyle =\frac{16-14}{\sqrt{10}/\sqrt{5}} \)
\( \displaystyle =\frac{2}{\sqrt{2}}=\sqrt{2}\approx 1.414 \)
(The other common form, with \( s=\sqrt{\frac{40}{5}}=\sqrt{8} \) and \( t=\frac{\bar{x}-\mu}{s/\sqrt{n-1}}=\frac{2}{\sqrt{8}/2} \), gives the same value \( \sqrt{2} \).)