Respuesta :
Answer:
[tex]p_v = P(z>2.425) = 0.0076[/tex]
The p value is a value in order to reject or not the null hypothesis. If the p value is higher than the significance level we FAIL to reject the null hypothesis otherwise we have enough evidence to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
X=152 represent the people passed the exam
[tex]\hat p = \frac{152}{200}= 0.76[/tex] estimated proportion of people report having texted while driving
[tex]p_o = 0.68[/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 true proportion is higher than 0.68.:
Null hypothesis:[tex]p \leq 0.68[/tex]
Alternative hypothesis:[tex]p>0.68[/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{0.76 -0.68}{\sqrt{\frac{0.68(1-0.68)}{200}}}=2.425[/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 left right test the p value would be:
[tex]p_v = P(z>2.425) = 0.0076[/tex]
The p value is a value in order to reject or not the null hypothesis. If the p value is higher than the significance level we FAIL to reject the null hypothesis otherwise we have enough evidence to reject the null hypothesis.
The p value in the probability shows that the instructor should not believe the success rate has improved.
How to calculate the probability?
From the information given, the sample proportion will be:
= 152/200 = 0.76.
The value to be tested is 0.68. The test statistic is 2.425. Therefore, the p value is 0.0076.
In this case, the p value indicates that there no difference between the observed proportion and samples proportion. Therefore, the instructor should not believe the success rate has improved.
Learn more about probability on:
https://brainly.com/question/24756209
