To obtain information on the corrosionresistance properties

To obtain information on the corrosion-resistance properties of a certain type of steel conduit. 45 specimens arc buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of X bar = 52.7 and a sample standard deviation of s = 4.8. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. Is there compelling evidence for concluding that true average penetration exceeds 50 mils Carry out a test of hypotheses using a significance level of 5%. What is the test statistic t = 3.77 No, z = 3.77 Yes, z = 3.77

Solution

17.

We use z distribution, as n = 45 > 30.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   50  
Ha:    u   >   50  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    52.7          
uo = hypothesized mean =    50          
n = sample size =    45          
s = standard deviation =    4.8          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.773364712 =3.77          
              
As z > 1.6449, we   REJECT THE NULL HYPOTHESIS.  

Hence,

OPTION C: YES, Z = 3.77 [ANSWER, C]