A
Andrea
Guest
The Bureau of Economic Analysis in the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $18,688 (USA Today, August 24, 1995).
A researcher for the state of North Carolina wants to test the following hypothesis:
Where μ is the mean annual income for a resident of North Carolina.
The researcher gathers information from a sample of 625 residents of North Carolina and finds a sample mean of 17,076 with a sample standard deviation equal to 15,500.
a.What is the appropriate conclusion pertaining to the hypothesis formulated above? Use a 0.01 level of significance.
b.What is the ρ-value for this test? What is the conclusion in part a, if you want to use p-value approach?
c.Construct a 99% Confidence Interval for the value of the mean pertaining to the North Carolina residents’ income based on that sample mean gathered by the researcher (But use the Standard Deviation of the Population).
d.How would your answer to part a. change if the sample size, instead of 625, were 25? (Assuming you do NOT know the Standard Deviation of the Population). Demonstrate and Explain.
e.How would your answer to part d. change if you KNEW the value of the standard deviation of the population? That is, you are answering to part a, by relaying on a sample size of n=25, and standard Deviation of the population equal to $15,500.
f.How would your answer to part a. change if, you were only concerned (or worried) whether the average income reported by the Bureau of Economic Analysis might overestimate the true value of mean annual income for a resident of North Carolina?
A researcher for the state of North Carolina wants to test the following hypothesis:
Where μ is the mean annual income for a resident of North Carolina.
The researcher gathers information from a sample of 625 residents of North Carolina and finds a sample mean of 17,076 with a sample standard deviation equal to 15,500.
a.What is the appropriate conclusion pertaining to the hypothesis formulated above? Use a 0.01 level of significance.
b.What is the ρ-value for this test? What is the conclusion in part a, if you want to use p-value approach?
c.Construct a 99% Confidence Interval for the value of the mean pertaining to the North Carolina residents’ income based on that sample mean gathered by the researcher (But use the Standard Deviation of the Population).
d.How would your answer to part a. change if the sample size, instead of 625, were 25? (Assuming you do NOT know the Standard Deviation of the Population). Demonstrate and Explain.
e.How would your answer to part d. change if you KNEW the value of the standard deviation of the population? That is, you are answering to part a, by relaying on a sample size of n=25, and standard Deviation of the population equal to $15,500.
f.How would your answer to part a. change if, you were only concerned (or worried) whether the average income reported by the Bureau of Economic Analysis might overestimate the true value of mean annual income for a resident of North Carolina?