Mathematics, 20.04.2020 20:19, mia3128

According to an exit poll for an election, 55.6% of the sample size of 836 reported voting for a specific candidate. Is this enough evidence to predict who won? Test that the population proportion who voted for this candidate was 0.50 against the alternative that it differed from 0.50.

Report the test statistic and P-value and interpret the latter.

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answered: hawleyemily

$z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238$

p_v =2*P(z3.238)=0.0012

The p value is a reference value and is useful in order to take a decision for the null hypothesis is this p value is lower than a significance level given we reject the null hypothesis and otherwise we have enough evidence to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

n=836 represent the random sample taken

$\hat p=0.556$ estimated proportion of interest

p_o=0.5 is the value that we want to test

$\alpha$ represent the significance level

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 ture proportion is equal to 0.5 or no.:

Null hypothesis: p=0.5

Alternative hypothesis: $p \neq 0.5$

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 .

Calculate the statistic

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

$z=\frac{0.556 -0.5}{\sqrt{\frac{0.5(1-0.5)}{836}}}=3.238$

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 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(z3.238)=0.0012

answered: Guest

Line the mark up so you will find your answer

answered: Guest

Iwould like to think so. what’s the question you need with?

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According to an exit poll for an election, 55.6% of the sample size of 836 reported voting for a spe...