Questions: Use the answer key to determine that you accurately determined and interpreted errors in hypothesis testing. - If necessary, revise your work. 1. Census data reveal that the ownership rate in one small city is around 59%. 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. a. What are the hypotheses? b. What would a type I error be in this test? c. What would a type II error be in this test?

Use the answer key to determine that you accurately determined and interpreted errors in hypothesis testing.
- If necessary, revise your work.
1. Census data reveal that the ownership rate in one small city is around 59%. 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.
a. What are the hypotheses?
b. What would a type I error be in this test?
c. What would a type II error be in this test?

Transcript text: - Use the answer key to determine that you accurately determined and interpreted errors in hypothesis testing. - If necessary, revise your work. 1. Census data reveal that the ownership rate in one small city is around $59 \%$. 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. a. What are the hypotheses? b. What would a type I error be in this test? c. What would a type II error be in this test? © Success Academy Charter Schools

Solution

Solution Steps

Step 1: Define the hypotheses

The null hypothesis $ H_0 $ represents the status quo, which is that the home ownership rate has not increased. The alternative hypothesis $ H_1 $ represents the claim that the home ownership rate has increased.

$ H_0: p = 0.59 $
$ H_1: p > 0.59 $

Step 2: Define Type I error

A Type I error occurs when we reject the null hypothesis $ H_0 $ when it is actually true. In this context, it would mean concluding that the home ownership rate has increased when, in reality, it has not.

Step 3: Define Type II error

A Type II error occurs when we fail to reject the null hypothesis $ H_0 $ when it is actually false. In this context, it would mean failing to conclude that the home ownership rate has increased when, in reality, it has.

Final Answer

a. $ H_0: p = 0.59 $, $ H_1: p > 0.59 $
b. Concluding that the home ownership rate has increased when it has not.
c. Failing to conclude that the home ownership rate has increased when it has.

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