A company manufactures light bulbs and wants to advertise a

A company manufactures light bulbs and wants to advertise a mean life of 1200 hours for the light bulbs. To support this, the company randomly sampled of 36 light bulbs. If the t values fall in the 90% confidence interval for the population, the company will be satisfied that it is manufacturing acceptable light bulbs. The mean of the sample is found to be 1178 hours and the standard deviation is 35 hours. Can the company advertise a mean life of 1200 hours; are they making acceptable light bulbs? Explain your reasoning.

Solution

Set Up Hypothesis
Null, H0: U=1200
Alternate, H1: U<1200
Test Statistic
Population Mean(U)=1200
Sample X(Mean)=1178
Standard Deviation(S.D)=35
Number (n)=36
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1178-1200/(35/Sqrt(35))
to =-3.771
| to | =3.771
Critical Value
The Value of |t | with n-1 = 35 d.f is 1.306
We got |to| =3.771 & | t | =1.306
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -3.7714 ) = 0.0003
Hence Value of P0.1 > 0.0003,Here we Reject Ho

No, they are n\'t making acceptable light bulbs