Respuesta :
Answer:
[tex]z=\frac{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/tex]
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
Step-by-step explanation:
Data given and notation
n=250 represent the random sample taken
[tex]\hat p=0.44[/tex] estimated proportion of of the readers owned a particular make of car.
[tex]p_o=0.53[/tex] is the value that we want to test
[tex]\alpha=0.05[/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 porportion is equal to 0.53.:
Null hypothesis:[tex]p=0.53[/tex]
Alternative hypothesis:[tex]p \neq 0.53[/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{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/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.
The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
