Question

You want to test if more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction. You take a sample of 60 homes from this neighborhood and find that 14 fit your criteria. The appropriate null and alternative hypotheses are _______________________.

Answer 1

We need to conduct a hypothesis in order to test the claim that more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction, so then the correct system of hypothesis are:

Null hypothesis:
`p \leq 0.2`

Alternative hypothesis:
`p > 0.2`

Explanation:

Data given and notation

n=60 represent the random sample taken

X=14 represent the neighborhood that have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction

`\hat p=(14)/(60)=0.233` estimated proportion of neighborhood that have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction

`p_o=0.2` is the value that we want to test

`\alpha` represent the significance level

z would represent the statistic (variable of interest)

`p_v` represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that more than 20% of homes in a neighborhood have recently been sold through a short sale, at a foreclosure auction, or by the bank following an unsuccessful foreclosure auction, so then the correct system of hypothesis are:

Null hypothesis:
`p \leq 0.2`

Alternative hypothesis:
`p > 0.2`

When we conduct a proportion test we need to use the z statistic, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

The One-Sample Proportion Test is used to assess whether a population proportion
`\hat p` is significantly different from a hypothesized value
`p_o`.