ECON 2330 stats 2

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ECON 2330 Assignment#1

Note: You may use Excel or any other software to do some calculations for these questions. But in order to get full mark, you must show the answers in a way that I can simply follow the steps to get the same answers you arrived at. Then save your works as a PDF file and upload it using the dropbox in Moodle under Assignment#1.

1) Home values tend to increase over time under normal conditions, but

the recession of 2008 and 2009 has reportedly caused the sales price of existing homes to fall nationwide (Businessweek, March 9, 2009). You would like to see if the data support this conclusion. The file HomePrices from Chapter 10 (available on Moodle) contains data on 30 existing home sales in 2006 and 40 existing home sales in 2009.

a) Provide a point estimate of the difference between the population mean prices for the two years.

b) Develop a 99% confidence interval estimate of the difference between the resale prices of houses in 2006 and 2009.

c) Would you feel justified in concluding that resale prices of existing homes have declined from 2006 to 2009? Why or why not?

2) Vacation occupancy rates were expected to be up during March 2008 in

Myrtle Beach, South Carolina (The Sun News, February 29, 2008). Data in the file Occupancy from Ch10 which is available on Moodle will allow you to replicate the findings presented in the newspaper. The data show units rented and not rented for a random sample of vacation properties during the first week of March 2007 and March 2008.

a) Estimate the proportion of units rented during the first week of March 2007 and the first week of March 2008.

b) Provide a 95% confidence interval for the difference in proportions. c) On the basis of your findings, does it appear March rental rates for

2008 will be up from those a year earlier?

3) Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of

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$170 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100.

a) State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

b) At a .01 level of significance, what is your conclusion? What is the p- value? Discuss the reasonableness of your findings.

4) The estimated daily living costs for an executive traveling to various major

cities given below. The estimates include a single room at a four-star hotel, beverages, breakfast, taxi fares, and incidental costs.

a) Compute the sample mean. b) Compute the sample standard deviation. c) Compute a 95% confidence interval for the population standard

deviation.

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5) The variance in a production process is an important measure of the

quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. The data Bags is available on Moodle under Chapter 11. Use a 0.05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

6) The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. At a 5% level of significance, test to determine if there has been a significant decrease in the average price of homes.

a)

State the null and alternative hypotheses to be

b) Compute the test statistic.

c) Determine the critical value for this test.

d) What do you conclude?

e) Compute the p-value.

7) Before the last presidential debates, 50% of registered votes indicated they were planning to vote for the incumbent president. In a recent poll of 1200 registered voters after the debates, 636 indicated they are planning to vote for the incumbent president. Has there been a significant increase in the proportion of registered voters who are planning to vote for the incumbent president?

a)

State the null and alternative hypotheses to be tested.

b) Compute the test statistic.

c)

The null hypothesis is to be tested using α = 0.05. Determine the critical value(s) for this test.

d) What do you conclude?

e) Compute the p-value.

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