Light bulbs are supposed to last for 3000 hours with a stand

Light bulbs are supposed to last for 3000 hours with a standard deviation of 65 hours. The quality control engineer samples 49 light bulbs and finds that they last for an average of 2934 hours. Test to determine if the average life of the bulbs is significantly less than the stated life of 3000 hours using = 0.05.

Solution

Set Up Hypothesis
Null, H0: U=3000
Alternate,life of the bulbs is significantly less than the stated life of 3000 hours H1: U<3000
Test Statistic
Population Mean(U)=3000
Sample X(Mean)=2934
Standard Deviation(S.D)=65
Number (n)=49
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =2934-3000/(65/Sqrt(48))
to =-7.108
| to | =7.108
Critical Value
The Value of |t | with n-1 = 48 d.f is 1.677
We got |to| =7.108 & | t | =1.677
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -7.1077 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

We have evidence that life of the bulbs is significantly less than the stated life of 3000 hours