Mathematics, 15.04.2020 04:56 jaylaa04

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: emmavaran03

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

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 interest 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 successes

$\hat p=\frac{765}{1500}=0.51$ estimated proportion of successes

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

parallel and congruent

step-by-step explanation:

the movement of translation is linear. these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope! you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

Answer from: Quest

im alright what do you need

step-by-step explanation:

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Suppose a poll is taken that shows that 765 out of 1500 randomly selected, independent people believ...