Answer to Question #229195 in Statistics and Probability for Rup

Question

a shopkeeper claims that the average life of CFL bulb is 1600 hours.to check this claim a researcher takes a sample of 100 CFL bulbs of tha same make randomly and finds mean lifetime of 1570 hours with standard daviation of 120 hours.is tha claim acceptable at 5% level of significance?

Answer 1

$n=100 \\ \bar{x}=1570 \\ \sigma= 120 \\ H_0: \mu=1600 \\ H_1: \mu≠1600$

Test-statistic:

$Z = \frac{\bar{x} - \mu }{\sigma/ \sqrt{n}} \\ = \frac{1570-1600}{120/ \sqrt{100}} \\ = -2.5 \\ α=0.05 \\$

Two-tailed test.

Reject H₀ if Z ≤1.96 or Z≥1.96.

$Z=-2.5 < Z_c=-1.96$

We are able to reject H₀.

The population mean lifetime of bulbs is not equal to 1600 hours at 0.05 significance level.