An Izod impact test was performed on 20 specimens of PVC pip

An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1. 0 ft-lb/in. The sample average and standard deviation obtained were x = 1. 121 and s = 0. 328, respectively. Test H0: mu = 1. 0 versus H1:mu > 1. 0 using alpha = 0. 01 and draw conclusions. State any necessary assumptions about the underlying distribution of the data. Consider the Izod impact strength problem described. Construct a 90% PI for the impact strength of a single specimen of PVC pipe. Find a tolerance interval for the impact strength that includes 95% of the specimens in the population with 95% confidence.

Solution

Set Up Hypothesis
Null, H0: U=1
Alternate,Impact strength greater than 1 H1: U>1
Test Statistic
Population Mean(U)=1
Sample X(Mean)=1.121
Standard Deviation(S.D)=0.328
Number (n)=20
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1.121-1/(0.328/Sqrt(19))
to =1.65
| to | =1.65
Critical Value
The Value of |t | with n-1 = 19 d.f is 2.539
We got |to| =1.65 & | t | =2.539
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.6498 ) = 0.05771
Hence Value of P0.01 < 0.05771,Here We Do not Reject Ho

Impact strength greater than 1