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 33 coins was collected. Those coins have a mean weight of 2.49498 g and a standard deviation of 0.01899 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? Identify the test statistic.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=2.5
Alternate, H1: U!=2.5
Test Statistic
Population Mean(U)=2.5
Sample X(Mean)=2.49498
Standard Deviation(S.D)=0.01899
Number (n)=33
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =2.49498-2.5/(0.01899/Sqrt(33))
to =-1.519
| to | =1.519
Critical Value
The Value of |t | with n-1 = 32 d.f is 2.037
We got |to| =1.519 & | t | =2.037
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.5186 ) = 0.1387
Hence Value of P0.05 < 0.1387,Here We Do not Reject Ho

[ANSWER]
Test statistic: to =-1.519

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