1. John Mode had been offered a job in a midsized east Texas town. Obviously, the cost of housing in this city will be an important consideration in a decision to move. John read an article in the paper from the town in which they presently live that claimed the "average" price of home was $155,000. John wants to know whether the data collected in "DATATAB 1_2" indicate a difference between the two cities. They assumed that the "average" price referred to in the article was the mean, and the sample they collected from the new city represents a random sample of all home price in that city. Based on the information, conduct hypothesis testing by calculating required test statistics following the steps mentioned below (consider price in 1000 for simplicity): (6 points). a) State the null and alternative hypothesis. Specify whether this is two-tailed test with justification. b) Calculate the sample standard deviation using excel spreadsheet. c) Calculate t score using sampled standard deviation D @ 70F HD 3 c) Calculate t score using samplea stangara deviation. d) Test the null hypothesis at significance level 0.1, 0.05, and 0.01. e) Interpret your results. f) Compute a 0.95 confidence interval on the mean house price $ 141.4 and comment on the result if this interval contains the average mean price. 2. A local congressman indicated that he would support the building of a new dam on the O 70F et 00% Y Normal text Times New... - - 12 + BIVA GD DE 2 3 4 5 6 Yahoo River if more than 60% of his constituents supported the dam. His legislative aide sampled 225 registered voters in his districts and found 148 favored the dam. (4 points) a) Set up the null and alternative hypothesis. b) At the 0.1 significance level, should the congressman support the building of the dam? c) How many voters should the aide sample if the congressman wanted to estimate the true level of support to within 1% using a 95% confidence interval? d) Construct a 90% confidence interval for the proportion of all registered voters in the district who favor the dam. varchi 70