Question
In: Statistics and Probability
Assume that a simple random sample has been selected from a normally distributed population and test...
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 32 coins was collected. Those coins have a mean weight of 2.49543 g and a standard deviation of 0.01598 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?
Solutions
Expert Solution
Solution :
Given that,
Population mean = 
= 2.5
Sample mean = 
= 2.49543
Sample standard deviation = s = 0.01598
Sample size = n = 32
Level of significance = 
= 0.05
This is a two tailed test.
The null and alternative hypothesis is,
Ho:
2.5
Ha:
2.5
The test statistics,
t = ( -
)/ (s/
)
= ( 2.49543 - 2.5 ) / ( 0.01598 / 
32)
= -1.618
p-value = 0.1158
The p-value is p = 0.1158 and since p = 0.1158 ≥ 0.05, it is concluded that the null hypothesis is fails to reject.
C0nclusion:
It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to claim that A coin mint
has a specification that a particular coin has a mean weight is different than 2.5, at the 0.05 significance level.
orchestra answered 1 year agoRelated Solutions
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