A sample of 45 observations is selected from a normal population. The sample mea
ID: 3133128 • Letter: A
Question
A sample of 45 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.10 significance level. H0: = 51 H1: 51 12. value: 10.00 points Required information a. Is this a one- or two-tailed test? One-tailed test Two-tailed test References eBook & Resources Multiple ChoiceDifficulty: 2 IntermediateLearning Objective: 10-05 Conduct a test of a hypothesis about a population mean. Check my work 13. value: 10.00 points Required information b. What is the decision rule? Reject H0 if z < -1.645 or z > 1.645 Reject H0 if -1.645 < z < 1.645 References eBook & Resources Multiple ChoiceDifficulty: 2 IntermediateLearning Objective: 10-05 Conduct a test of a hypothesis about a population mean. Check my work 14. value: 10.00 points Required information c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic References eBook & Resources WorksheetDifficulty: 2 IntermediateLearning Objective: 10-05 Conduct a test of a hypothesis about a population mean. Check my work 15. value: 10.00 points Required information d. What is your decision regarding H0? Fail to reject H0 Reject H0 References eBook & Resources Multiple ChoiceDifficulty: 2 IntermediateLearning Objective: 10-05 Conduct a test of a hypothesis about a population mean. Check my work 16. value: 10.00 points Required information e. What is the p-value? (Round z value to 2 decimal places and final answer to 4 decimal places.) p-value
Explanation / Answer
a) Since the alternative hypothesis claims that mu is not equal to 51, without indicating any direction, it is two tailed test.
b) From information given, Xbar=49, Sigma=5, n=45, mu=51. Substitute the valuesin following equation to obtain the z test statistic value.
z=(Xbar-mu)/(Sigma/sqrt n)=(49-51)/(5/sqrt 45)=-2.68
c) The test is two-tailed and z (critical) at alpha=0.10 is +-1.645. Decision rule is: Reject H0 if z(observed) is less than -1.645 or z(observed) >1.645.
d) The test statistic falls in critical region. Therefore, reject H0.
e) The p value is 0.0073.