A random sample of residents will be obtained and asked

Question

1. The Dallas, Texas, city council is going to consider a zoning variance for the Estates on Frankford apartment complex so that the developer may extend the structure closer to the nearest road. Some council members are concerned about safety, but they will vote for the measure if more than 0.79 million of the city residents favor the variance. A random sample of residents will be obtained and asked whether they favor the zoning variance

a) State the null and alternative hypotheses.

b) In context, explain what the Type I error is.

c) In context, explain what the Type II error is.

d) Which one is worse for the city council members, Type I error or Type II error? Why?

2. Suppose U.S. monetary policy will be set by the Federal Reserve Board by examining the average consumer price, for a large fixed set of common commodities. The Board will raise the interest rate if there is evidence that the average price is less than $125.50. A random sample of counties will be obtained, and the cost of these goods in each county will be used to test the relevant hypothesis.

a) State the null and alternative hypotheses.

b) In context, explain what the Type I error is.

c) In context, explain what the Type II error is.

d) Mortgage rates will rise if the Board raises interest rates. Which one is worse for home buyers, Type I error or Type II error? Why?

3. Consider a hypothesis test concerning a population mean with s known and n large. For each of the following situations, calculate the p-value and determine if H₀ is rejected at a 5% significance level with the already computed test statistic z_ts = 1.92.

a) H₀: μ = 694  H_a: μ > 694

b) H₀: μ = 186  H_a: μ < 186

c) H₀: μ = 337  H_a: μ ¹ 337