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 .

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:  

Alternative hypothesis:  

Step-by-step 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

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

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

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:  

Alternative hypothesis:  

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

(1)  

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

answer is:

1.75 pounds