Business, 07.01.2020 10:31 LanaParrilla

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?

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Answer from: kaitlyn1152

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

$p_v =2*P(z6.35)=2.15x10^{-10}$

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:

$p_v =2*P(z6.35)=2.15x10^{-10}$

Answer from: Quest

the answer is d

explanation:

Answer from: Quest

explanation:

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