The weights of a simple random sample of 35 pennies have a m

The weights of a simple random sample of 35 pennies have a mean of 0.3910 g and a standard deviation of .04 g. Use a .05 significance level to test that all pennies have weights with a mean greater than 0.230 g.

State the null and alternative hypotheses, the pvalue, and conclusion.

Thanks for the help!

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   0.23  
Ha:    u   >   0.23   [ANSWER, HYPOTHESES]

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As we can see, this is a    right   tailed test.      
                      
Getting the test statistic, as              
              
X = sample mean =    0.391          
uo = hypothesized mean =    0.23          
n = sample size =    35          
s = standard deviation =    0.04          
              
Thus, z = (X - uo) * sqrt(n) / s =    23.81222113          
              
Thus, the p value is              
              
p =    1.2477*10^-125 [VERY CLOSE TO 0] [ANSWER, P VALUE]

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As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that all pennies have weights with a mean greater than 0.230 g. [CONCLUSION]