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.

And we have a left tailed test for this case

Step-by-step explanation:

Data given and notation

n represent the random sample taken

estimated proportion of interest

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

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:  

Alternative hypothesis:  

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

(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

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:  

And we have a left tailed test for this case