An electrician wants to prove that mean = the average life in hours of a light b

Question

An electrician wants to prove that mean = the average life in hours of a light bulb is more than 1000 hours. Suppose that a random sample of 101 light bulbs shows an average life of 1038 hours, with a sample standard deviation of 103 hours. Assume that the lives of light bulbs are normally distributed.

a. State the name of the Test you will use and Assumptions for your Test.

b. State the null and the alternative hypothesis [VERBALLY AND MATHEMATICALLY].

C. State the test statistic.

d. Compute the test statistic

e. Draw the rejection region (just draw it and put alpha and the critical value on the appropriate places).

f. Compute the critical value and the P-value.

g. Based on the critical value and P-value what is your conclusion and interpret.

Explanation / Answer

Set Up Hypothesis
Null,average life in hours of a light bulb is equal to 1000 H0: U=1000
Alternate,average life in hours of a light bulb is more than 1000 H1: U>1000
Test Statistic
Population Mean(U)=1000
Sample X(Mean)=1038
Standard Deviation(S.D)=103
Number (n)=101
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1038-1000/(103/Sqrt(101))
to =3.708
| to | =3.708
Critical Value
The Value of |t | with n-1 = 100 d.f is 1.66
We got |to| =3.708 & | t | =1.66
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 3.7077 ) = 0.00017
Hence Value of P0.05 > 0.00017,Here we Reject Ho

We have evidence that average life in hours of a light bulb is more than 1000

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