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...

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 60% of all city residents favor the variance. A random sample of residents will be obtained and asked whether they favor the zoning variance. Let p be the true proportion of residents who favor the extended structure.

a. State the null and alternative hypotheses in terms of p.

b. Describe a type I error and a type II error in this context.

 c. Which error is more serious for the developer? Why? d. Which error is more serious for the city council members? Why?

The National Fire Protection Association maintains an extensive list of codes and standards that address equipment, extinguishing systems, and fire-protective gear.13 A firefighter’s helmet should withstand a temperature of 1200°F for 30 seconds. The Seattle Fire Department is ordering helmets from Kidde Fire Fighting. They will accept the shipment only if there is no evidence to suggest the helmets fail to meet the standard. Let m be the mean temperature the helmets can withstand.

a. State the null and alternative hypothesis.

 b. Describe a type I error and a type II error in the context of this problem.