Answer to Question #195101 in Statistics and Probability for simon

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.

Answer 1

1) H₀: $\mu$ =1250 (claim)

H₁: $\mu$ $\neq$ 1250

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

3)

$$z=\frac{\overline{X}-\mu}{\sigma/\sqrt{n}}=\frac{1290-1250}{110/\sqrt{25}}=1.82$$

4) Since -1.96<z<1.96, the decision is to not reject the null hypothesis.

5) There is enough evidence to support the claim.