Answer :
Answer:
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:
Null hypothesis:[tex]p=0.36[/tex]
Alternative hypothesis:[tex]p \neq 0.36[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>2.074)=0.0381[/tex]
Step-by-step explanation:
Data given and notation n
n represent the random sample taken
[tex]\hat p[/tex] estimated proportion of interest
[tex]p_o=0.36[/tex] is the value that we want to test
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 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:
Null hypothesis:[tex]p=0.36[/tex]
Alternative hypothesis:[tex]p \neq 0.36[/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 is significantly different from a hypothesized value .
Calculate the statistic
For this case the statistic is given:
[tex] z = 2.074[/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>2.074)=0.0381[/tex]