Assume that a simple random sample has been selected from a normally distributed

Question

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 2.5 g. A sample of 35 coins was collected. Those coins have a mean weight of 2.49573 g and a standard deviation of 0.01751 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the coins appear to conform to the specifications of the coin mint? What are the hypotheses? OA. Ho: #2.5 g ( C. Ho: = 2.5 g O B. Ho: = 2.5 g H1 : 22.5g Ho: = 2.5 g H1 : #2.5 g H1: = 2.5 g D. H1:

Explanation / Answer

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

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As we can see, this is a    2   tailed test.  
          

df = n - 1 =     34      

          
Getting the test statistic, as          
          
X = sample mean =    2.49573      
uo = hypothesized mean =    2.5      
n = sample size =    35      
s = standard deviation =    0.01751      
          
Thus, t = (X - uo) * sqrt(n) / s =    -1.442699068 [ANSWER, ITEM 2]

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Also, the p value is          
          
p =    0.158255253 [ANSWER, ITEM 3]

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Comparing z and zcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.

There is insufficient evidence to warrant rejection of the claim that u = 2.5. [OPTION C]      

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