Time Remaining: 04:20.27 Submit C This Question: 1 pt 17017(1 complete) This Qui
ID: 3350202 • Letter: T
Question
Time Remaining: 04:20.27 Submit C This Question: 1 pt 17017(1 complete) This Quiz: 7pts poss 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 2.5g. A sample of 35 coins was collected. Those coins have a mean weight of 2.49623 g and a standard deviation of 0.01496 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? OA, OB, Ho : -25g H1: H225g OD, Ho: . 2.5 g H1 :Explanation / Answer
Solution:-
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 = 0.00253
DF = n - 1 = 35 - 1
D.F = 34
t = (x - ) / SE
t = - 1.49
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 34 degrees of freedom is less than -1.49 or greater than 1.49.
Thus, the P-value = 0.145
Interpret results. Since the P-value (0.145) is greater than the significance level (0.05), we cannot reject the null hypothesis.
D) Fail to reject H0, There is insufficient evidence to warrant rejection of the claim that the sample is from population with mean weight equal to 2.5g.
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