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 37 coins was collected. Those coins have a mean weight of 2.49574 g and a standard deviation of 0.01147 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? Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. *I am mainly having trouble with finding the p-value. I can't figure out how to get it.*

Explanation / Answer

Given that,
population mean(u)=2.5
sample mean, x =2.49574
standard deviation, s =0.01147
number (n)=37
null, Ho: =2.5
alternate, H1: !=2.5
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.028
since our test is two-tailed
reject Ho, if to < -2.028 OR if to > 2.028
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.49574-2.5/(0.01147/sqrt(37))
to =-2.259
| to | =2.259
critical value
the value of |t | with n-1 = 36 d.f is 2.028
we got |to| =2.259 & | t | =2.028
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -2.2592 ) = 0.03
hence value of p0.05 > 0.03,here we reject Ho

ANSWERS
---------------
null, Ho: =2.5
alternate, H1: !=2.5
test statistic: -2.259
critical value: -2.028 , 2.028
decision: reject Ho
p-value: 0.03

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