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.

In words, what will their hypotheses be?

Answer 1

Null Hypothesis,
`H_0` : p = 67.4%

Alternate Hypothesis,
`H_A` : p > 67.4%

Explanation:

We are given that 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.

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.

Let p = percentage of American families owned their homes or the rate of home ownership

So, Null Hypothesis,
`H_0` : p = 67.4%

Alternate Hypothesis,
`H_A` : p > 67.4%

Here, null hypothesis states that the rate of home ownership remains the same after 2-year trial basis.

On the other hand, alternate hypothesis states that the rate of home ownership is increasing after 2-year trial basis.

Hence, this would be the appropriate hypothesis.

Answer 2

The hypothesis can be defined as follows:

H₀: The rate of home ownership is 67.4%, i.e. p = 0.674.

Hₐ: The rate of home ownership is more than 67.4%, i.e. p > 0.674.

Step-by-step explanation:

In this case we need to determine whether the city should continue with plan of offering tax breaks to first-time home buyers in order to encourage people to become homeowners.

It is provided that, a few years ago, a census bureau reported that 67.4% of American families owned their homes.

But the Census data reveal that the ownership rate in one small city is much lower.

So, to improvise this the city council wants 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.

To determine whether the city council should continue with the plan or not, the hypothesis can be defined as follows:

H₀: The rate of home ownership is 67.4%, i.e. p = 0.674.

Hₐ: The rate of home ownership is more than 67.4%, i.e. p > 0.674.