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Analysis of Practice Questions in Statistics

## Question 1: Home Prices between 2006 and 2009

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 in2009.

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 and2009.
c) Would you feel justified in concluding that resale prices of existing homes have declined from 2006 to 2009? Why or why not?

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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 March2008.

a) Estimate the proportion of units rented during the first week of March 2007 and the first week of March2008.
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?

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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 2\$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 0.01 level of significance, what is your conclusion? What is the p- value? Discuss the reasonableness of your findings.

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4) 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 ofhomes.

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.

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5) According to YCharts in 2018, the unemployment rate for 15- to 24-yearolds in British Columbia was reported to be 9.4% for July, 2018 specifically.
Suppose that this report was based on a random sample of four hundred 15- to 24-year-olds. A political campaign manager wants to know if the sample results can be used to conclude that the unemployment rate for 15- to 24-year-old British Columbians is significantly higher than the unemployment rate for all adults in British Columbia based on a significance level ?=0.05. According to the Statistics Canada, the unemployment rate for all adults in British Columbia was 5.0% in July 2018.

a) State the hypotheses.
b) Calculate the test statistic.
c) Find the p-value.
d) What is your hypothesis test decision?
e) What is your conclusion in the context of the application? The conclusion should relate back to the question.