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 775 hours. A random sample of 71 light bulbs has a mean life of 763 hour a standard deviation of 80 hours. Do you have enough evidence to reject the manufacturer\'s claim? Use alpha = 0.0 Identify the null hypothesis and alternative hypothesis. (Use a comma to separate answers as needed Round to two decimal places as needed.)

Solution

Set Up Hypothesis
Null, H0: U>=775
Alternate, H1: U<775
Test Statistic
Population Mean(U)=775
Sample X(Mean)=763
Standard Deviation(S.D)=80
Number (n)=71
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =763-775/(80/Sqrt(71))
to =-1.264
| to | =1.264
Critical Value
The Value of |t | with n-1 = 70 d.f is 2.381
We got |to| =1.264 & | t | =2.381
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.2639 ) = 0.10523
Hence Value of P0.01 < 0.10523,Here We Do not Reject Ho

[ANSWERS]
to =-1.26

Here we don\'t have the Population standard deviation given, we use T-test.