The Bureau of Economic Analysis in the U.S. Department of Commerce reported that the mean annual...

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Statistics

The Bureau of Economic Analysis in the U.S. Department ofCommerce reported that the mean annual income for a resident ofNorth Carolina is $18,688 (USA Today, August 24, 1995). Aresearcher for the state of South Carolina wants to see if the meanannual income for a resident of South Carolina is different. Asample of 400 residents of South Carolina shows a sample meanannual income of $16,860 and the population standard deviation isassumed to known, ï³ =$14,624. Use a 0.05 level of significance, theresearcher wants to test the following hypothesis.
H0: ï = 18,688 Ha: ï ï‚¹ 18,688
a) Use confidence interval approach to test the hypothesis?
b)What is your conclusion?
C)What are three rejection rules (You have used confidenceinterval approach in Question 2)?
D)Do three rejection rules lead to the same conclusion? What isyour conclusion?

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3.6 Ratings (330 Votes)

Let X be the annualincomeLet n be the sample sizeNull and alternative hypothesesareHo 18688Ha 18688 X 16860Sample Meann 400Sample Size 14624Population Standard Deviation 005 2 0025a Confidence interval for mean is givenbyFor confidence See Answer

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