Mathematics, 20.02.2020 08:12 brooklyn4682

8 with H1:p>0.75, a test statistic is z=0.55. use a 0.05 significance level to find the p value and state the conclusion about the null hypothesis

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Answer from: lilybrok04

p_v =P(z0.55)=0.2912

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.

Step-by-step explanation:

Data given and notation

n represent the random sample taken

$\hat p$ estimated proportion of interest

p_o=0.75 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 0.75.:

Null hypothesis: $p\leq 0.75$

Alternative hypothesis: p 0.75

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

The statistic calculated on this case is:

z= 0.55

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(z0.55)=0.2912

Answer from: Quest

step-by-step explanation:

Answer from: Quest

don't report but were is the digram

step-by-step explanation:

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