Question:2x²-5x+3 <br>answer:

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we don't have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the population proportion of extroverts among college student government leaders is not different from 0.82.

Step-by-step explanation:

1) Data given and notation

n=74 represent the random sample taken

X=57 represent the number of people found extroverts

$\hat p=\frac{57}{74}=0.770$ estimated proportion of people found extroverts.

$p_o=0.82$ 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 if population proportion of extroverts among college student government leaders is different (either way) from 82%, the system of hypothesis would be on this case:

Null hypothesis: $p= 0.82$

Alternative hypothesis: $p \neq 0.82$

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 $p_o$ .

3) Calculate the statistic

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

$z=\frac{0.770 -0.82}{\sqrt{\frac{0.82(1-0.82)}{74}}}=-1.12$

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:

$p_v =2*P(z$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we don't have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the population proportion of extroverts among college student government leaders is not different from 0.82.

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3 years ago

Question:2x²-5x+3 answer:​

Question:2x²-5x+3 answer: