Answer to Question #107479 in Statistics and Probability for justine

Question

A light-bulb manufacturer regularly advertises that his bulbs last 900 hours with a standard deviation of 75 hours. A random sample is chosen before each campaign to make sure that the claim is correct. A sample of 200 bulbs shows a mean of 925 hours. Can the advertising’s claim be considered an underestimate at the 0.05 level of significance?

Answer 1

$Ho: \mu=900\\ Ha: \mu>900$

Test statistic is given by

$\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}=$

$=\frac{925-900}{\frac{75}{\sqrt{200}}}=4.714$

From z table or =NORM.S.INV(0.95) Excel formula, the critical value is 1.645. Since test statistic is greater than the critical value, we reject the null hypothesis and conclude that the advertising claim is an underestimate.