Question

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.57. With H1 : p < 0.57 you obtain a test statistic of z = − 2.858 . Use a normal distribution calculator and the test statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.

Answer 1

`p_v =P(z<-2.858)=0.0021`

And we have a left tailed test for this case

Explanation:

Data given and notation

n represent the random sample taken

`\hat p` estimated proportion of interest

`p_o=0.57` is the value that we want to test

`\alpha` represent the significance level

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 less than 0.57 or no:

Null hypothesis:
`p\geq 0.57`

Alternative hypothesis:
`p < 0.57`

When we conduct a proportion test we need to use the z statisitc, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic

The statistic for this case is given
`z_(calc)= -2.858`

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 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<-2.858)=0.0021`

And we have a left tailed test for this case