Suppose a student measuring the boiling temperature of a liquid observes the reading in (degree Celsius) 102.5, 101.7, 103.1, 100.9, 100.5 and 102.2 of 6 different samples of a liquid. If margin of error is 0.96 calculate confidence interval.

(100.86, 102.78)

The correct answer is Option (2) → (100.86, 102.78)

Mean, $\bar x=\frac{102.5+101.7+103.1+100.9+100.5+102.2}{6}$

$=101.83°C$

Standard deviation, $s=\sqrt{\frac{∑(x_i-\bar x)^2}{n-1}}$

$s=\sqrt{\frac{4.7971}{6-1}}=0.9795°C$

Confidence interval = $\bar x±\left(t_{r/2}+\frac{s}{\sqrt{n}}\right)$

$=101.23±0.96$

∴ Interval = (100.86, 102.78)°C