The u. s. department of transportation estimates that 10% of americans carpool. does that imply that 10% of cars will have two or more occupants? a sample of 300 cars traveling southbound on the new jersey turnpike yesterday revealed that 63 had two or more occupants. at the 0.01 significance level, can we conclude that 10% of cars traveling on the new jersey turnpike have two or more occupants?

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of cars that had two or more occupants is significantly different from 0.1 or 10%.  

Explanation:

1) Data given and notation

n=300 represent the random sample taken

X=63 represent the number of cars that had two or more occupants

estimated proportion of cars that had two or more occupants

is the value that we want to test

represent the significance level

Confidence=99% or 0.959

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the true proportion of cars that had two or more occupants is 0.1:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

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 significance level provided . The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of cars that had two or more occupants is significantly different from 0.1 or 10%.  

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