Mathematics, 14.04.2020 17:20 marie1211

Suppose a poll is taken that shows that 765 out of 1500 randomly selected, independent people believe the rich should pay more taxes than they do. Test the hypothesis that a majority (more than 50%) believe the rich should pay more taxes than they do. Use a significance level of 0.05.

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Answer from: xcoder1732

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

p_v =P(z0.775)=0.219

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 independent people who believe the rich should pay more taxes than they do is not significantly higher than 0.5

Step-by-step explanation:

Data given and notation

n=1500 represent the random sample taken

X=765 represent the independent people who believe the rich should pay more taxes than they do

$\hat p=\frac{765}{1500}=0.51$ estimated proportion of independent people who believe the rich should pay more taxes than they do

p_o=0.5 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 higher than 0.5.:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: p 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:

$z=\frac{0.51 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1500}}}=0.775$

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 right tailed test the p value would be:

p_v =P(z0.775)=0.219

Answer from: Quest

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

Answer from: Quest

chiken

step-by-step explanation:

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