Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. If α = 0.05, test the manufacturer's claim.

Answer 1

Solution :

= 1000

= 980

s = 80

n = 25

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 1000

Ha : 1000  

Test statistic = t

= ( - ) / s  / n

= (980 - 1000) /80 / 25

= -1.25

P (Z < -1.25 ) = 0.2234

P-value = 0.2234

= 0.05  

0.2234 >  0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that