A shipping firm suspects that the mean life of a certain bra

A shipping firm suspects that the mean life of a certain brand of tire used by Its trucks IS lest than 40.000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 39.300 miles with a standard deviation of 1200 miles. At a = 0.05. test the shipping firm\'s claim. Round the test statistic to the nearest thousandth. Use classical approach. Step 1: state the hypothesis. Step 2: Find the critical value. Step 3: Compute the test statistics. Sketch the standard normal distribution and indicate critical and test statistics. Make a decision and state the conclusion.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=40000
Alternate Hypothesis H1: U<40000
Test Statistic
Population Mean(U)=40000
Given That X(Mean)=39300
Standard Deviation(S.D)=1200
Number (n)=18
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=39300-40000/(1200/Sqrt(18)
Zo =-2.4749
| Zo | =2.4749
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.4749 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -2.4749 ) = 0.0067
Hence Value of P0.05 > 0.0067, Here we Reject Ho

Mean life of certain brand of tire used by trucks is less than 40000