Answer to Question #278428 in Statistics and Probability for brad

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

 

Find the sample mean x.

Answer 1

Given $H_o$ = 650 hour.

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

$\begin{aligned} \\ \text { Sample mean } &=\left(\frac{\sum x}{n}\right) \\ &=\left(\frac{6392}{50}\right) \text { hours. } \\ &=127.84 \text { hours. } \end{aligned}$