Respuesta :
Answer:
We need to conduct a hypothesis in order to test the claim that the true proportion os homeowners who have a home security alarm is less than 0.17 or 17%, so then we need to conduct a left tailed test and the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.17[/tex]
Alternative hypothesis:[tex]p < 0.17[/tex]
Step-by-step explanation:
Data given and notation
n represent the random sample taken
[tex]\hat p[/tex] estimated proportion of interest
[tex]p_o=0.17[/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 the true proportion os homeowners who have a home security alarm is less than 0.17 or 17%, so then we need to conduct a left tailed (since we want to check if the real parameter is lower than specified value) test and the system of hypothesis are.:
Null hypothesis:[tex]p\geq0.17[/tex]
Alternative hypothesis:[tex]p < 0.17[/tex]
When we conduct a proportion test we need to use the z statisitc, 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].
