1. Sample data about the listing price of a house is collected from Surrey, Guilford area in 2022 and the data is given below. Using the data answer the following questions: N 1 2 3 4 5 6 7 8 Listing Price 1049900 11 1229000 1049900 12 1230000 1050000 13 1298999 1075000 14 1299000 1075000 15 1299000 1078800 16 1398000 1179000 17 1398000 1188000 18 1399000 1188000 19 1449900 1225000 20 1450000 a. What is the mean listing price of a home? b. Generate appropriate numerical summaries for the listing price of a home, the sample standard deviation, etc. 9 10 Listing Price N Listing Price 21 1450000 22 1450000 23 1469900 24 1475000 25 1475000 26 1480000 27 1499000 28 1499000 29 1499233 30 1499900 N C. Use these summaries to develop a 95% confidence interval to estimate the mean listing price of a house in your selected city. That is, you will be using the sampling data you collected to estimate the population parameter (listing price). Make sure to show both your calculations and a final statement of its meaning. d. The mean selling price of a house in the sample area is said to be $1,400,00. To determine if this is true in your sample data, conduct a hypothesis test using a critical value approach using a = 0.05 level of significance. Make sure to state the null and alternative hypotheses. Write a concluding statement about your results. 2. Grace is the manager at a local restaurant and has implemented changes to her operation to reduce the average wait time for a table between 6pm and 8pm on Saturday night to less than 20 minutes. A random sample of 45 wait times on Saturday night had a mean of 18.3 minutes. Grace knows from past experience that the standard deviation of wait times is 5 minutes. Conduct a hypothesis test using p-value and critical value approach to determine if Grace's changes have reduced average wait time to less than 20 minutes using a = 0.01 3. Business organizations are relying more and more on social media to search job candidates. According to one survey, 70% of employers use social media sites to screen job candidates during hiring process. A random sample of 160 firms found that 103 of them use social media sites to screen candidates during the hiring process. Test the hypothesis that less than 70% of organizations use social media to screen job candidates during the hiring process with a = 0.01. a. use the critical value approach to test this hypothesis b. use the p-value approach to test this hypothesis