As a recent graduate, you have been looking for jobs throughout New York State. Last week, you received a job offer from a company that is located in Philadelphia. After careful consideration, you decided to accept this job offer. As a result, you have to sell your current home in Latham to prepare for the move. You contact a real estate agent to begin the process of selling your current home. You provide the following information to the agent: your home is 2235 square feet, has 2.5 baths, and 3 bedrooms. There is a 4th bedroom that you converted to a study but can easily be converted back to a bedroom. In addition, the basement is finished and has a half bath; therefore, it may serve as an additional bedroom. The real estate agent suggests that you list your house for $305,000. You want to make sure that the real estate agent lists your house at a price consistent with the other houses for sale in your town. In order to verify this information, you go to the Times Union classifieds and look at all the homes listed for sale in Latham that have between 3 and 5 bedrooms. You take a simple random sample of 30 of these homes and summarize the data in a table, which is attached to this assignment. You will use this data to perform a number of calculations and make a conclusion about whether or not the real estate agent has the house listed at a fair price based on the data that you collected. Project Calculations III. Inferential Statistics - Testing a Mean Price and Estimating a Mean Price 1. Perform a t-test to determine if the average price of comparable homes in Latham is different than the $305,000 recommended by the real estate agent. Perform a two- sided t-test. a. b. C. d. e. f. 8. Write the appropriate hypotheses. Write the assumptions required for the test. Calculate the test statistic. (Use the Descriptive Statistics command on EXCEL to obtain the sample mean and standard deviation.) Calculate the p-value. Explain what the p-value means in this situation. What is your decision if the significance level a = 0.05? Write a conclusion. 2. Calculate a 95% confidence interval for the mean price of comparable houses based on your sample mean. What can you say about the average price of comparable homes based on the confidence interval? Sample Data House 1 23 5 6 7 8 69 9 10 11 12 13 14 15 16 17 18 19 20 21 22 22222222 23 24 25 26 27 28 29 30 # Bedrooms 3 wwwwwwwwww 3 3 3 3 3 3 3 3 3 3 3334 4 4 4 4 4 4 4 4 55 4 4 #Bathrooms 2 2.5 2.5 22222 2.5 2 2.5 2 2 2.5 222 2.5 2.5 2.5 2.5 2.5 2.5 NNNNNNNMM 6323 3 2.5 2 5555 2.5 2.5 3.5 3.5 3.5 2.5 Square Feet 1550 1614 1715 1758 1794 1860 1877 1900 1911 1921 1921 2015 2118 2351 1800 2083 2100 2112 2112 2210 2260 2400 2416 2444 2600 3159 3200 3200 2580 3300 Price $329,744 $259,000 $295,100 $309,500 $282,900 $296,950 $219,000 $349,900 $374,900 $314,360 $314,360 $369,900 $395,342 $321,900 $209,900 $275,000 $309,900 $317,750 $317,750 $279,699 $295,500 $239,900 $374,900 $331,900 $369,900 $463,055 $479,000 $470,000 $389,900 $559,000