The quality control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a larger shipment of CFL is equal to 7,500 hours.
The population standard deviation is 1,200 hours.
A random sample of 64 CFLs indicates a sample mean life of 7,250 hours.
At the 0.05 level of significance, is there evidence that the mean life is different from 7,500 hours?
H0:
=7500
Ha:
7500
Sample size, n =64
Sample mean,
=7250
Population standard deviation,
= 1200
Standard error of
, SE(
)
=
=1200//8 =120
Test statistc, Z= ()
/
= (7250-7500)/120 =-25/12= -2.083
At
Zcrit= 1.96
|Z| =2.083>1.96
So,reject null hypothesis. There is enough evidence to conclude that Mean life is different from 7500 hours.
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