Mathematics, 15.04.2020 00:17, badpotterchris

Historically, the percentage of residents of a certain country who support stricter gun control laws has been 54%. A recent poll of 906 people showed 504 in favor of stricter gun control laws. Assume the poll was given to a random sample of people. Test the claim that the proportion of those favoring stricter gun control has charged. Perform a hypothesis test, using significance level of 0.05

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answered: manaisialockhart12

$z=\frac{0.556 -0.54}{\sqrt{\frac{0.54(1-0.54)}{906}}}=0.966$

p_v =2*P(z0.966)=0.334

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people in favor of stricter gun control laws is not significantly different from 0.54 or 54%

Step-by-step explanation:

Data given and notation

n=906 represent the random sample taken

X=504 represent the people in favor of stricter gun control laws

$\hat p=\frac{504}{906}=0.556$ estimated proportion of people in favor of stricter gun control laws

p_o=0.54 is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

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 different from 0.54 or no:

Null hypothesis: p=0.54

Alternative hypothesis: $p \neq 0.54$

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:

$z=\frac{0.556 -0.54}{\sqrt{\frac{0.54(1-0.54)}{906}}}=0.966$

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 $\alpha=0.05$ . 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(z0.966)=0.334

answered: Guest

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