Respuesta :
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:[tex]p \leq 0.2[/tex]
Alternative hypothesis:[tex]p > 0.2[/tex]
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
[tex]\hat p=\frac{14}{60}=0.233[/tex] 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
[tex]p_o=0.2[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] 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:[tex]p \leq 0.2[/tex]
Alternative hypothesis:[tex]p > 0.2[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
