Answer to Question #107758 in Statistics and Probability for Sonali

Question

The xyz manufacturing bulbs hypothesis that the life of bulbs is 145 hours with a known standard deviation of 210 hours. A random sample of 25 bulbs give A mean life of 130 hours. Using 0.05 level of significance, can the co. Conclude that the mean life of bulbs is less than 145 hours?

Answer 1

Null hypothesis $H_0 :\mu=145.$

Alternative hypothesis $H_a: \mu<145$.

Test statistic: $z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{130-145}{\frac{21}{\sqrt{25}}}=-3.57.$

P-value: $p=0.0002.$

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

We can conclude that the mean life of bulbs is less than 145 hours.