Respuesta :
Answer:
[tex]z=\frac{0.57 -0.6}{\sqrt{\frac{0.6(1-0.6)}{100}}}=-0.612[/tex]
[tex]p_v =2*P(z<-0.612)=0.5405[/tex]
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
X=57 represent the subscribers indicated that they planned to renew their subscriptions
[tex]\hat p=\frac{57}{100}=0.57[/tex] estimated proportion of subscribers indicated that they planned to renew their subscriptions
[tex]p_o=0.6[/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 current rate of renewals differs from the rate previously experienced, so the system of hypothesis are:
Null hypothesis:[tex]p=0.6[/tex]
Alternative hypothesis:[tex]p \neq 0.6[/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{0.57 -0.6}{\sqrt{\frac{0.6(1-0.6)}{100}}}=-0.612[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-0.612)=0.5405[/tex]
