A security expert claims that less than 17% of all homeowners have a home security alarm. State Upper H 0 and Upper H Subscript a in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.

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].

A security expert claims that less than 17​% of all homeowners have a home security alarm. State Upper H 0 and Upper H Subscript a in words and in symbols. Then determine whether the hypothesis test for this claim is​ left-tailed, right-tailed, or​ two-tailed. Explain your reasoning.

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A security expert claims that less than 17% of all homeowners have a home security alarm. State Upper H 0 and Upper H Subscript a in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.