4 Historically a particular variety of tomato plant has had

4. Historically, a particular variety of tomato plant has had a standard deviation of 6 days for ripening time. This year a hybrid variety of 41 plants had a standard deviation of 4.5 days. Use a 5% level of significance to test the claim that these tomatoes are ripening closer together than they were previously.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   <=   6  
Ha:    sigma   >   6  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha =    0.05          
df = N - 1 =    40          
chi^2 (crit) =    55.75847928        
              
Getting the test statistic, as              
s = sample standard deviation =    4.5          
sigmao = hypothesized standard deviation =    6          
n = sample size =    41          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    22.5          
              
Comparing chi^2 < chi^2(crit), we FAIL TO REJECT THE NULL HYPOTHESIS.          

There is no signficant evidence that these tomatoes are ripening closer together than they were previously. [conclusion]