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

Question

Assume that a simple random sample has been selected from a normlly distributed population and test the given claim. Identfy the null and altemative 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 2.49387 g and a standard deviation of 0.01349 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 specfications of the coin mint? O B. Ho: =2.5 g H1 : >2.5 g Ho : 2.5 g H1 : #2.5 g A. Ho: #2.5 g H1 : =2.5 g Ho: = 2.5 g H1 :

Explanation / Answer

Question 1

(a) Hypothesis ar e

H0 : = 2.5 g

Ha : 2.5 g

sample mean x = 2.49387 g

sample standard deviation s = 0.01349 g

sample size n = 32

standard error for the sample mean se0 = s/ n = 0.01349/ 32 = 0.002385 g

Test statistic

t - (x - H)/ se0 = (2.49387 -2.5)/  0.002385 = -2.571

P- value = Pr(t > 2.57; dF = 32-1 = 31; Two tailed) = 0.0152 < 0.05

Here we shall reject the null Hypothesis. There is sufficient evidence to warrant rejection of the claim that the sample is from a population of mean weight equal to 2.5 gm.

Option A is correct,

- The next question is

Here also Optioon A is correct as he it may seems that coins may come from a population with mean weight different form 2.5 g.

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