Mathematics, 07.04.2020 23:34 treavonknorton

Trials in an experiment with a polygraph include 98 results that include 23 cases of wrong results and 75 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

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Answer from: yam78

$z=\frac{0.765 -0.8}{\sqrt{\frac{0.8(1-0.8)}{98}}}=-0.866$

p_v =P(z

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ 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 1% of significance the proportion of correct cases is not significantly lower than 0.8 or 80%

Step-by-step explanation:

Data given and notation

n=98 represent the random sample taken

X=75 represent the number of correct cases

$\hat p=\frac{75}{98}=0.765$ estimated proportion of correct cases

p_o=0.8 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

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 proportions is lower than 0.8 or not.:

Null hypothesis: $p \geq 0.8$

Alternative hypothesis: p < 0.8

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:

$z=\frac{0.765 -0.8}{\sqrt{\frac{0.8(1-0.8)}{98}}}=-0.866$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

p_v =P(z

Answer from: Quest

im alright what do you need

step-by-step explanation:

Answer from: Quest

answer: 5

step-by-step explanation:

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