Respuesta :
Answer:
[tex]p_v =P(Z<-2.246)=0.0124[/tex]
Step-by-step explanation:
1) Data given and notation
n represent the random sample taken
X represent the number of items with the charcteristics desired
[tex]\hat p[/tex] estimated proportion of items with the charcteristics desired
[tex]p_o=0.65[/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)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the proportion is less than 65%:
Null hypothesis:[tex]p\geq 0.65[/tex]
Alternative hypothesis:[tex]p < 0.65[/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].
3) Calculate the statistic
The statistic on this case is given Z=-2.246
4) 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 left tailed test the p value would be:
[tex]p_v =P(Z<-2.246)=0.0124[/tex]
