Mathematics, 09.04.2020 02:59 lmoleary7466

70% of the U. S. population recycles. According to a green survey of a random sample of 250 college students, 204 said that they recycled. At alpha = 0.01, is there sufficient evidence to conclude that the proportion of college students who recycle is greater than 70%?

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Answer from: maddieg5585

$z=\frac{0.816 -0.7}{\sqrt{\frac{0.7(1-0.7)}{250}}}=4.002$

p_v =P(z4.002)=0.0000314

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 people said that they recycled is significantly higher than 0.7 or 70%

Step-by-step explanation:

Data given and notation

n=250 represent the random sample taken

X=204 represent the people said that they recycled

$\hat p=\frac{204}{250}=0.816$ estimated proportion of people said that they recycled

p_o=0.7 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v 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 0.7.:

Null hypothesis: $p\leq 0.7$

Alternative hypothesis: p 0.7

When we conduct a proportion test we need to use the z statisitc, 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 .

Calculate the statistic

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

$z=\frac{0.816 -0.7}{\sqrt{\frac{0.7(1-0.7)}{250}}}=4.002$

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 right tailed test the p value would be:

p_v =P(z4.002)=0.0000314

Answer from: Quest

explanation:

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

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