Answer to Question #210942 in Statistics and Probability for afg

Question

A factory manufacturing light-emitting diode (LED) bulb claims that their light bulbs last for 50,000 hours on the average. To confirm if this claim was valid, a quality control manager got a sample of 50 LED bulbs and obtained a mean lifespan of 40,000 hours. The standard deviation of the manufacturing process is 20,000 Do you think the claim of the manufacturer is valid at the 5% level of significance? 

Answer 1

$\bar{x}=40000 \\ s=20000 \\ n=50 \\ df=n-1=49 \\ α=0.05 \\ H_0: \mu=50000 \\ H_1: \mu ≠50000 \\ t_{crit}=2.095$

The rejection region for this two-tailed test is R={t:|t|>2.0095}

Test-statistic:

$t = \frac{\bar{x}- \mu}{s/ \sqrt{n}} \\ t = \frac{40000-50000}{20000 / \sqrt{50}} = -3.535 \\ |t|=3.535>2.0095$

The null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is different than 50000, at the 0.05 significance level.