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

Answer:

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:$p > 0.2$  

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

$\hat p=\frac{14}{60}=0.233$ 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:  

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

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