Question 280464: Test the hypothesis that the population average income in an area I am interested in is greater than $55,000. If I can show that the mean is indeed greater than that amount I intend to open an up-scale restaurant that, by past experience, will probably be successful. If the average income is less than $55,000 my restaurant will probably fail.I am going to take a large sample, n=121, and of course money is ratio level data. My initial thought is to use an alpha of 5%Assume that when I do a sample I get a sample mean of $55,450 and a sample standard deviation of $2,500.Test the hypotheses using the full 5-step process. State your conclusion in statistical terms and in conversational English. Compute the p-value What effect might a different alpha value have?Discuss the type I and type II errors and what they mean in this situation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Test the hypothesis that the population average income in an area I am interested in is greater than $55,000. If I can show that the mean is indeed greater than that amount I intend to open an up-scale restaurant that, by past experience, will probably be successful. If the average income is less than $55,000 my restaurant will probably fail.I am going to take a large sample, n=121, and of course money is ratio level data. My initial thought is to use an alpha of 5%Assume that when I do a sample I get a sample mean of $55,450 and a sample standard deviation of $2,500.Test the hypotheses using the full 5-step process. State your conclusion in statistical terms and in conversational English. Compute the p-value What effect might a different alpha value have?Discuss the type I and type II errors and what they mean in this situation.
Ho: u <= 55000
Ha: u > 55000
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t(55450) = (55450-55000)/[2500/sqrt(121)] = 1.98
p-value = p(t > 1.98 with df = 120) = 0.0250
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Reject Ho at the 5% significance level;
Fail to reject Ho at the 1% significance level:
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Type I ERROR: You reject Ho and therefore conclude the mean salary is
above 55000. So you open your store and it fails because the salaries
are really < 55000.
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Type II ERROR: You fail to reject Ho. You don't open your store and
you miss out on having a successful business because the salaries
really are above 55000.
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Cheers,
Stan H.
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