Question

A few years​ ago, a census bureau reported that​ 67.4% of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. The city council is debating a plan to offer tax breaks to​ first-time home buyers in order to encourage people to become homeowners. They decide to adopt the plan on a​ 2-year trial basis and use the data they collect to make a decision about continuing the tax breaks. Since this plan costs the city tax​ revenues, they will continue to use it only if there is strong evidence that the rate of home ownership is increasing.

Who would be harmed by a Type II error?

(A) The city, because it would lose tax revenue. Faster pace
(B) The citizens of the city, because they lose help they could have used to buy a home.
(C) The city, because it would lose homeowners.
(D) The citizens of the city, because they would have to pay higher taxes than before.
(E) There is no Type Il error in this context.

Answer 1

(B) The citizens of the city, because they lose help they could have used to buy a home.

Explanation:

Nul and alternative hypotheses are:

• 
  `H_(0):` the rate of home ownership is the same after tax cut

• 
  `H_(a):` the rate of home ownership is increasing after tax cut

Type II error occurs when one fails to reject null hypothesis when the null hypothesis was wrong.

In this case Type II error happens when the conclusion is the rate of home ownership is not increasing after tax cut, where actually it is.

With this conclusion city council does not continue tax cut, and citizens of the city is harmed because they lose help they could have used to buy a home.