(Chapter 10) As a real estate agent, Marty was given 20 homes to sell. He thought that he was not fairly assigned the homes to sell because the price average of his homes to sell is much below the...

(Chapter 10) As a real estate agent, Marty was given 20 homes to sell. He thought that he was not fairly assigned the homes to sell because the price average of his homes to sell is much below the average of all homes sold by the real estate. (hint: compute his homes’ price mean and the all homes price mean to see the difference). He believes that all agents must be assigned to sell homes with the mean price closed to the mean price of all homes sold by the real estate company. His argument centers on the fact that all agents are paid a 3% commission from the price of homes that they sell. For example, if he sells a $300,000 home, his commission is $9,000. Another agent, Peterson is assigned $900,000 plus home so Peterson's commission is more than $27,000. The home price in the dataset follows the normal probability distribution. Based on Marty’s home prices and at a 0.05 significance level, is it reasonable to conclude that Marty is assigned to sell homes with an average price less than the average price of all homes? (hint: you must find out the population size, the population means, population standard deviation, sample size, the sample mean, and z test statistic. Follow the steps of hypothesis testing to derive your conclusion). Answer the following questions: 1.1 (5 points) State the null hypothesis and the alternate hypothesis 1.2 (5 points) Identify the test statistic (hint: population standard deviation is known) 1.3 (5 points) Find out the critical value (hint: make sure you know whether a one-tailed or two-tailed test to use Student’s t distribution table) 1.4 (5 points) Formulate the decision rule (hint: draw a normal curve to mark the critical value) 1.5 (5 points) Compute the test statistic (hint: the formula is listed in the textbook’s Chapter 10 and Chapter 10’s Part 1 and Part 2 lecture videos) 1.6 (5 points) State your decision: Reject or not to reject the null hypothesis 1.7 (5 points) State your conclusion about Marty’s fairness claim 2. (Chapter 11) Using the dataset as the sample to represent the population of homes in general and at 0.05 significance level, can we conclude that there is a difference in the mean selling price of homes in general with a fixed mortgage and homes with an adjustable mortgage? It is assumed that both populations’ price of fixed and adjustable mortgages are approximately normally distributed and they have equal and unknown standard deviations. (hint: find out the sample sizes, sample variances, pooled variances, and t-test statistic. Follow the steps of hypothesis testing to arrive at your conclusion). Answer the following questions: 2.1 (5 points) State the null hypothesis and the alternate hypothesis 2.2 (5 points) Identify the test statistic (hint: population standard deviation is unknown) 2.3 (5 points) Find out the critical value (hint: find the degree of freedom and make sure you know whether a one-tailed or two-tailed test to use Student’s t distribution table) 2.4 (5 points) Formulate the decision rule (hint: draw a normal curve to mark the critical value) 2.5 (10 points) Compute the test statistic (hint: the formula is listed in the textbook’s Chapter 11 and Chapter 11’s Part 1 lecture video) 2.6 (5 points) State your decision: Reject or not to reject the null hypothesis 2.7 (5 points) State your conclusion about the mean of the selling price between fixed mortgage homes and adjustable-mortgage homes.