Question

Through careful record keeping, you have the times to burn out of 100 Bright brand light bulbs. The average time to burn out is 200 hours, with a standard deviation of 12 hours. Give a 95% confidence interval for the mean time to burn out of this brand of light bulb.

Answer 1

The critical value for $\alpha = 0.05$ and $df = n-1 = 99$ degrees of freedom is (using critical values table)

$t_c = z_{1-\alpha/2; n-1} = 1.984$

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-t_c\times\dfrac{s}{\sqrt{n}},\bar{x}+t_c\times\dfrac{s}{\sqrt{n}})$$ $$=(200-1.984\times\dfrac{12}{\sqrt{100}},200+1.984\times\dfrac{12}{\sqrt{100}})$$ $$=(197.62,202.38)$$

Therefore, based on the data provided, the 95% confidence interval for the population mean is $197.62 < \mu < 202.38,$ which indicates that we are 95% confident that the true population mean $\mu$ is contained by the interval $197.62, 202.38).$