An egg packaging comppany has stated that the standard devia

An egg packaging comppany has stated that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. The sample variance for 51 eggs was 0.0065 ounces. Can this sample result comfirm the company\'s claim? Use x(level of signifcance)=0.1

Can you provide the working so that I can get a clearer understanding of the answer? Thanks

Solution

Here,

s = sqrt(0.0065) = 0.080622577.

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   >=   0.07  
Ha:    sigma   <   0.07  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.1   ,      
alpha =    0.1          
df = N - 1 =    50          
chi^2 (crit) =    37.68864839        
              
Getting the test statistic, as              

s = sample standard deviation =    0.080622577          
sigmao = hypothesized standard deviation =    0.07          
n = sample size =    51          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    66.32653061          
              
Comparing chi^2 > chi^2(crit), we FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the standard deviation of the weights of their grade A large eggs is 0.07 ounces or less. [CONCLUSION]