Respuesta :
Answer:
[tex]z=\frac{0.62 -0.5}{\sqrt{\frac{0.5(1-0.5)}{570}}}=5.730[/tex]
Step-by-step explanation:
Data given and notation
n=570 represent the random sample taken
[tex]\hat p=0.62[/tex] estimated proportion of adults with the characteristic
[tex]p_o=0.5[/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 true proportion is higher than 0.5.:
Null hypothesis:[tex]p \leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/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{0.62 -0.5}{\sqrt{\frac{0.5(1-0.5)}{570}}}=5.730[/tex]
