Answer to Question #331163 in Statistics and Probability for rose

Question

The General Electric Company claims that the life of LED light bulbs are has a mean life of 500 hours with the standard deviation of 50 hours. Test the claim of the manufacture if a random sample of 80 LED light tested and found out to be 450 hours only. Use 5% level of significance.​

Answer 1

$H_0:\mu=500.$

$H_a:\mu \ne 500.$

Test statistic: $z=\frac{450-500}{\frac{50}{\sqrt{80}}}=-8.94.$

P-value: $p=2P(Z<-8.94)<0.0001.$

Since the p-value is less than 0.05, reject the null hypothesis.

There is a sufficient evidence that the claim of the manufacture is not correct.