Question

The packaging on an electric light bulb states that the average length of life of bulbs is 1000 hours. A consumer association thinks that this is an overestimate and tests a random sample of 64 bulbs, recording the life x

 hours, of each bulb. The results are summarised as follows:

∑x=63910.4,∑x2=63824061

 

Calculate an unbiased estimate for the standard deviation of the length of life of all light bulbs of this type.

Answer 1

Given $H_o$ = 650 hour.

$n=50\ bulbs \quad, \sum x=6392 \quad \sum x^{2}=62424060.$

Standard deviation $=\frac{\sigma}{\sqrt{n}}=\frac{1}{n}\sqrt{\left.\frac{1}{n}\left(\sum x_i-n\right)^{2}\right) }$

$=\frac{1}{\sqrt{7}} \sqrt{\frac{\sum x^{2}}{n}-x^{-2}} =\sqrt{\frac{(62424060)}{50 \times 50}-\frac{(6312)^{2}}{\left(50^{3}\right)}}$

$=156.98$