Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 65%. With Ha : p < < 65% you obtain a test statistic of z = − 2.246 z=-2.246. Find the p-value accurate to 4 decimal places. p-value =

Answer 1

`p_v =P(Z<-2.246)=0.0124`

Explanation:

1) Data given and notation

n represent the random sample taken

X represent the number of items with the charcteristics desired

`\hat p` estimated proportion of items with the charcteristics desired

`p_o=0.65` is the value that we want to test

`\alpha` represent the significance level

z would represent the statistic (variable of interest)

Alternative hypothesis:
`p < 0.65`

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{(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`.

3) Calculate the statistic

The statistic on this case is given Z=-2.246

4) 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<-2.246)=0.0124`