For Problems #1 through #9, consider the following information: According to an undated press release from a regional association of realtors, the mean sales price of an existing, single family, free-standing home in this section of the country is $424,000. A random sample of the selling prices for 144 such houses in this area is collected by an officer in the organization because some believe the information is now outdated; there is concern the prices have changed substantially since that claim was made. The sample mean sales price is $426,450; the population standard deviation is known to be $12,000. At the 1% level of significance, or in other words, testing with 99% confidence, is it reasonable to conclude that the information may indeed be outdated and that the mean selling price is different than what was publicized in the new release? [HINTS: You should round any distribution values or standard scores and any probabilities to the nearest thousandth, if necessary.] #1: What are the null and alternative hypotheses, stated concisely with proper symbols? #2: What type of hypothesis test is involved: two-tail, one-tail left, or one-tail right? Explain. #3: Which type of test statistic is generated (i.e., z or t or F or 2) and why? Explain. #4: Determine the critical value(s) that designate the rejection region(s). #5: Determine the value of the test statistic (i.e., z or t or F or 2). #6: Determine the p-value that corresponds to the test statistic. #7: Concisely state the technical conclusion using appropriate and complete statistical language. #8: Interpret the findings in complete thoughts/phrases and within the context of the problem. #9: Construct the corresponding confidence interval which affirms the conclusion