Respuesta :
Answer:
[tex]p_v =2*P(Z>2.4)=0.016[/tex]
And we can use the following excel code:
"=2*(1-NORM.DIST(2.4;0;1;TRUE))"
Step-by-step explanation:
1) Data given and notation
n represent the random sample taken
X represent the business students who have personal computers (PC's) at home
[tex]\hat p[/tex] estimated proportion of business students who have personal computers (PC's) at home
[tex]p_o=0.25[/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 claim that the true proportion is 0.25:
Null hypothesis:[tex]p=0.25[/tex]
Alternative hypothesis:[tex]p \neq 0.25[/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 [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
For this case the value of the statistic is given by z=2.4 and that's given.
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 bilateral test the p value would be:
[tex]p_v =2*P(Z>2.4)=0.016[/tex]
And we can use the following excel code:
"=2*(1-NORM.DIST(2.4;0;1;TRUE))"
