Question

The mean lifetime of a sample of 100 light tubes produced by a company is found to be 1570 hours with standard deviation of 80 hours. Test the hypothesis that the mean lifetime of the tubes produced by the company is 1600 hrs.

Answer 1

n=100, $\bar X=1570, \sigma=80$

We test the hypotheses ;

$H_0:\mu=1600$

$H_1:\mu≠1600$

Since the sample size is greater than 30 and the population standard deviation is known we use the z test.

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

=$\frac{1600-1570}{\frac{80}{\sqrt{100}}}$

=3.75

We take a level of significance of 1%.

The corresponding critical value is;

$Z_{\alpha/2}=2.5758$

If the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

|3.75|>2.5758

We reject the null hypothesis hypothesis in favor of the alternative hypothesis.

We are 99% confident that the population mean lifetime of bulbs is not equal to 1600 hours.