Use a t-test to test the claim about the population mean mu at the given level o
ID: 3270340 • Letter: U
Question
Use a t-test to test the claim about the population mean mu at the given level of significance alpha using the given sample statistics. Assume the population is normally distributed. Claim: mu notequalto 25: alpha = 0.01 Sample statistics: x bar = 21.3, s = 4.9, n = 12 What are the null and alternative hypothesis? Choose the correct answer below. A. H_0: mu greaterthanorequalto 25 H_a: mu 25 What is the value of the standardized test statistics? The standardized test statistic is (Round to two decimal places as needed.) What is the P-value of the test-statistic? P-value = (Round to two decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis.Explanation / Answer
The null hypothesis is the hypothesis of no difference, that means the null hypothesis is population mean is no different from 25. The alternative hypothesis is the tentative proposition that the researcher wants to establish means it is what the reseracher claims. Therefore, the alternative hypothesis implies that population mean is different from 25. In statistical notation the null and altrenative hypotheses are
H0:mu=25 and H1:mu=/=25
Going by the stated logic, options A, B and D are ruled out. The correct answer is option A.
The value of standardized test statistic is as follows:
For small sample size (n<30), and known sample standard deviation, use Student's t model with (n-1)=11 degrees of freedom and perform 1-sample t test for population mean.
t=(xbar-mu)/(s/sqrt n), where, xbar is sample mean, mu is population mean, s is sample standard deviation, and n is sample size.
=(21.3-25)/(4.9/sqrt 12)
=-2.62
Using technology the exact P value at 11 degrees of freedom is: 0.024.
Per rejection rule based on P value, reject null hypothesis if P value is less than alpha=0.01. Here, P value is not less than 0.01, therefore, fail to reject null. There is insufficient evidence to support the claim.
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