The Dallas, Texas, city council is going to consider a zoning variance for the E

Question

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?

Explanation / Answer

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

Ho: p <= 0.60
Ha: p > 0.60 [ANSWER]

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

A type I error is concluding that the true proportion of residents who favor the extended structure is greater than 60% (hence favoring the extended structure), when in fact, it is not.

A type II error is concluding that the true proportion of residents who favor the extended structure is not greater than 60% (hence not favoring the extended structure), when in fact, it is.

c. Which error is more serious for the developer? Why?

A type I error, because they will lose the chance of having the extended structure.

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

A type II error, they are concerned about the dangers the extended structure may introduce.

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