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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3