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 36 coins was collected. Those coins have a mean weight of 2.49438 g and a standard deviation of 0.01564 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 or does their mean differ? What are the hypotheses? O A. Ho: H 2.5 g O B. Ho: H 2.5 g H1: 2 2.5 g H H1: H 2.5 g O C. Ho: H 2.5 g O D. Ho: 2.5 g H1: H 2.5 g 2.5 g Identify the test statistic, t L Round to two decimal places as neede Identify the P-value. The P-value is (Round to three decimal places as needed.) State the final conclusion that addresses the oriainal claim. Choose the correct answer below.

Explanation / Answer

Solution:-

= 2.5, n = 36, xbar = 2.49438, s = 0.01564,

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 2.5

Alternative hypothesis: 2.5

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.0026067

DF = n - 1 = 36 - 1

D.F = 35

t = (x - ) / SE

t = - 2.16

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 45 degrees of freedom is less than - 2.16 or greater than 2.16.

Thus, the P-value = 0.0377

Interpret results. Since the P-value (0.0377) is less than the significance level (0.05), we have to reject the null hypothesis.

Reject H0, There is insufficient evidence to warrant rejection of the claim that the sample is from population with a mean weight equal to 2.5 g.

No, Since the coin seems to come from a population with a mean weight different from 2.5 g.

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