An assembly line produces widgets with a mean weight of 10 a

An assembly line produces widgets with a mean weight of 10 and a standard deviation of 0.200. A new process supposedly will produce widgets with the same mean and a smaller standard deviation. A sample of 20 widgets produced by the new method has a sample standard deviation of 0.126. At a significance level of 10%, can we conclude that the new process is less variable than the old? State appropriate null and alternative hypotheses. For June through September of 1999, the rainfall and yield per acre of cotton were measured for 8 farms in Texas. The results are tabulated below. Find a 95% confidence interval for the expected cotton yield of a farm that receives 15 inches of rain. A six-sided die is tossed 180 times with the following results. Is there strong evidence that the die is not fair? Use a significance level of 10%.

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   >=   0.2  
Ha:    sigma   <   0.2  
              
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 =    19          
chi^2 (crit) =    11.65091003        
              
Getting the test statistic, as              
s = sample standard deviation =    0.126          
sigmao = hypothesized standard deviation =    0.2          
n = sample size =    20          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    7.5411          
              
As chi^2 < chi^2(crit), then we REJECT THE NULL HYPOTHESIS.              

Thus, there is significant evidence that the new process is less variable than the old. [CONCLUSION]

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