The average greyhound can reach a top speed of 185 meters pe

The average greyhound can reach a top speed of 18.5 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 40 of her dogs ran, on average, 19.2 meters per second with a population standard deviation of 1.2 meters per second. With = 0.05, is her claim correct?

Select one:

a. Yes, because the test value 0.09 falls in the noncritical region.

b. No, because the test value 0.09 falls in the critical region.

c. Yes, because the test value 3.69 falls in the critical region.

d. No, because the test value 0.70 falls in the critical region.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   18.5  
Ha:    u   >   18.5  
              
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 =    19.2          
uo = hypothesized mean =    18.5          
n = sample size =    40          
s = standard deviation =    1.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.689323937 = 3.69          
              
As z = 3.39 > 1.644, then we REJECT HO.

Thus,

OPTION C: Yes, because the test value 3.69 falls in the critical region. [ANSWER, C]