Question

In six attempts it took a locksmith 9, 14, 7, 8 11, 5 seconds to open a certain kind of lock. Construct a 95% confidence interval for the average it takes the locksmith to open this kind of lock.

Answer 1

$\bar{x} = \frac{9 + 14 +7+8+11+5}{6} \\ = 9$

Standard deviation

$SD = 3.1623 \\ n = 6$

Degree of freedom

$df = n - 1 \\ = 6 - 1 \\ = 5$

we look into t-distribution table with df and with 95% confidence level

Critical value t = 2.571

Confidence interval formula:

$= \bar{x} ± \frac{t \times SD}{\sqrt{n}} \\ = 9 ± \frac{2.571 \times 3.1623}{\sqrt{6}} \\ = 9 ± 3.32 \\$

5.68 < μ < 12.32