Assume that a simple random sample has been selected from a

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A coin mint has a specification that a particular coin has a mean weight of 2.5g. A sample of 37 coins was collected. Those coins have a mean weight of 2.49595 g and a standard deviation of 0.01744 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g. Do the coins appear to conform to the specifications of the coin mint?

A. Upper H 0: Mu = 2.5g Upper H 1: Mu not = 2.5g

B. Upper H 0: Mu = 2.5 g Upper H 1: Mu greater than or = 2.5g

C. Upper H 0: Mu not = 2.5g Upper H 1: Mu = 2.5g

D. Upper H 0: Mu = 2.5g Upper H 1: Mu less than2.5g

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   2.5  
Ha:    u   =/   2.5   [OPTION A]

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As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    2.49595          
uo = hypothesized mean =    2.5          
n = sample size =    37          
s = standard deviation =    0.01744          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.412568133          
              
Also, the p value is              
              
p =    0.157782744          
              
Comparing z is between the two zcrit (or, p>0.05), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence that these coins did not come from a population with mean weight 2.5g. [CONCLUSION]