1.A random sample of 81 credits sales in a department store showed an average sale of $68.00. From past date, it is known that the standard deviation of the population is $27.00

a.First verify that the Central Limit Theorem Conditions(s) have been met, then construct a 90% confidence interval of the population mean.

b.Construct a 99% confidence interval of the population mean.

c.Justify in your own word the difference in the interval lengths from parts a & b (i.e why are they different?)

d.Generally speaking, if the sample size is increased, what impact does it have on the margin of error? On the confidence interval?

2. The average price of hottest sold in the U.S. in 2012 was $240,000. A sample of 144 homes sold in Chattanooga in 2012 showed an average price of $246,000. It is known that the standard deviation of the population is $36,000. We are interested in degerming whether or not the average price of homes sold in Chattanooga is significantly different than the national average.

a.Verify whether the Central Limit Theorem conditions are met.

b.Develop the null hypothesis and the alternative hypotheisi.

c.Calculate the test statistic.

d.Find the critical z value.

e.Draw a picture and state the rejection rule and your conclusion in the context of this problem.

f.What is the p-value for the test statistic.

3.A sample of 36 bags of sugar produced by Domain sugar producers showed an average of 2 pounds and ounces with a standard deviation of 7 ounces.

a.At 95% confidence, compute the margin of error and explain what it shows.

b.Determine a 95% confidence interval for the average weight of the population of bags of sugar produced by the company. Give the answer in once and at least two decimal places.

c.The bags of sugar produced are supposed to contain 2 pounds of sugar, but the company allows 1.5% higher or lower than the 2 pounds. Have they reached their goal? Explain why or why not by giving numerical facts.