Respuesta :
Answer:
[tex]z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015[/tex]
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
[tex]\hat p=0.3[/tex] estimated proportion of interest
[tex]p_o=0.45[/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 is 0.45.:
Null hypothesis:[tex]p=0.45[/tex]
Alternative hypothesis:[tex]p \neq 0.45[/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].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015[/tex]
