Mathematics, 26.03.2020 02:00 smady

A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school's students approved of the parking that was provided. After the change, the principal surveys an SRS of 200 of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal's claim at the

α=0.05

significance level.

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Answer from: liyahsmith9305

$z=\frac{0.415 -0.37}{\sqrt{\frac{0.37(1-0.37)}{200}}}=1.318$

p_v =P(z1.318)=0.0937

So the p value obtained was a very low 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 is NOT improved (higher than 0.37)

Step-by-step explanation:

Data given and notation

n=200 represent the random sample taken

X=83 represent the students said say that they approve of the new parking arrangement

$\hat p=\frac{83}{200}=0.415$ estimated proportion of students said say that they approve of the new parking arrangement

p_o=0.37 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 0.37.:

Null hypothesis: $p \leq 0.37$

Alternative hypothesis: p 0.37

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:

$z=\frac{0.415 -0.37}{\sqrt{\frac{0.37(1-0.37)}{200}}}=1.318$

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(z1.318)=0.0937

Answer from: Quest

5x+10 is the correct one

hope this

Answer from: Quest

35-60 students are taking math.

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A local high school makes a change that should improve student satisfaction with the parking situati...