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klio [65]
3 years ago
11

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?
Business
2 answers:
daser333 [38]3 years ago
6 0

Answer: I HAVE NO IDEA SORRYYYYYYYY

Explanation:

den301095 [7]3 years ago
5 0

Answer:

z=\frac{0.21 -0.1}{\sqrt{\frac{0.1(1-0.1)}{300}}}=6.35  

p_v =2*P(z>6.35)=2.15x10^{-10}  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v 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

\hat p=\frac{63}{300}=0.21 estimated proportion of cars that had two or more occupants

p_o=0.1 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.959

z would represent the statistic (variable of interest)

p_v 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:p=0.1  

Alternative hypothesis:p \neq 0.1  

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

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

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

3) Calculate the statistic  

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

z=\frac{0.21 -0.1}{\sqrt{\frac{0.1(1-0.1)}{300}}}=6.35  

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 \alpha=0.01. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z>6.35)=2.15x10^{-10}  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v 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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