Question

An electric bulb company manufacturing company claims that the bulbs produced by them have a mean life of 1250 hours. A random sample of 25 bulbs gives an average life of 1290 hours with standard deviation of of 110 hours. Use 5% level of significance and test the claim if bulb life follows is 1250 hours. ( t _{0.025 (24) =2.064).}

Answer 1

$H_0 : \mu = 1250hrs.$

$H_1 : \mu \ne 1250$

Since $\alpha = 0.05$ and the test is a two tailed test, the critical values are -1.96 and 1.96

z can be calculated as $z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}} = \dfrac{1290-1250}{\dfrac{110}{\sqrt{25}}} = 1.82$

The vale of $\alpha$ is less than the calculated value of z. Hence, Null Hypothesis is accepted.