Answer to Question #238148 in Statistics and Probability for Aroo

Question

The mean lifetime of a sample of 144 fluorescent light bulbs produced by a company is computed to be 170 hours with a standard deviation of 120 hours. Test the company's claim that its bulbs' mean life time is 200 hours at 0.05 significance level. H0 : = 1600 hours H1 : 1600 hours

Answer 1

$\bar{x} = 170 \\ s = 120 \\ n=144 \\ H_0: \mu = 200 \\ H_1: \mu ≠200$

Test-statistic:

$t=\frac{\bar{x} -\mu}{s/ \sqrt{n}} \\ t = \frac{170-200}{120 / \sqrt{144}} =\frac{-30}{10} = -3 \\ α= 0.05 \\ df=n-1 = 144-1 = 143$

Two-tailed test

From table:

$t_{α/2,df} = t_{0.05/2, 143} = +/-1.9767$

The decision rule is: Reject H₀ if t ≤ -1.9767 or if t ≥ 1.9767.

Since, $t=-3< t_{α/2,df}$

We reject H₀ at 0.05 level of significance.

Conclusion: There is NOT sufficient evidence to support the claim that $\mu = 200.$