A light bulb manufacturer guarantees that the mean life of a

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 950 hours. A random sample of 65 light bulbs has a mean life of 930 hours with a standard deviation of 95 hours. Do you have enough evidence to reject the manufacturer\'s claim? use a=0.04

Solution

Set Up Hypothesis
Null, light bulb is at least 950 hours H0: U>=950
Alternate,light bulb is at below 950 hours H1: U<950
Test Statistic
Population Mean(U)=950
Sample X(Mean)=930
Standard Deviation(S.D)=95
Number (n)=65
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =930-950/(95/Sqrt(64))
to =-1.697
| to | =1.697
Critical Value
The Value of |t | with n-1 = 64 d.f is 1.779
We got |to| =1.697 & | t | =1.779
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.6973 ) = 0.04725
Hence Value of P0.04 < 0.04725,Here We Do not Reject Ho

We have evidence to support light bulb is at least 950 hours