Rapid Radish kits advertise that they reach maturity in 40 d

\"Rapid Radish\" kits advertise that they reach maturity in 40 days A plant breeder is trying to develop an even faster radish strain. In her sample of 45 radish plants, the average time to maturity was 39 days, with a sample standard deviation of 2 days. Is there sufficient evidence for the plant breeder to claim that she has developed a faster radish strain?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   40  
Ha:    u   <   40  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    44          
tcrit =    -   1.680229977      
              
Getting the test statistic, as              
              
X = sample mean =    39          
uo = hypothesized mean =    40          
n = sample size =    45          
s = standard deviation =    2          
              
Thus, t = (X - uo) * sqrt(n) / s =    -3.354101966          
              
Also, the p value is              
              
p =    0.00082333          
              
Comparing t < tcrit (or, p < 0.05), we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence at 0.05 level that she has a faster radish strain. [CONCLUSION]