A machine Tills 12 ounce bottles with soda For the machine t

A machine Tills 12 ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.03 ounce. A sample of 10 bottles is selected, and the number of ounces of soda in each bottle is given. At a = 0.05, can w c reject the claim that the machine is functioning properly? Use the P -value method. Assume the variables is approximately normally distributed. State the hypotheses and identify the claim with the correct hypothesis.

Solution

We seek to prove that the machine is not functioning properly, so that is the alternative hypothesis:

Ho: u <= 0.03
H1: u > 0.03 [ANSWER]

Hence, as H1 used >, then this is a ONE TAILED, RIGHT TAILED TEST. [ANSWER]

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   <=   0.03  
Ha:    sigma   >   0.03  
              
As we can see, this is a    right   tailed test.      
              
df = N - 1 =    9          
              
Getting the test statistic, as              
s = sample standard deviation =    0.041311822          
sigmao = hypothesized standard deviation =    0.03          
n = sample size =    10          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    17.06666667          
Thus, the P value is

P = 0.047682161 [ANSWER, P VALUE]

As P < 0.05, WE REJECT Ho. [ANSWER]

Thus, there is significant evidence at 0.05 level that the standard deviation is above 0.03. [ANSWER]