Gary is specifically interested in the π = the proportion of the non-face brick. Gary would like to do a hypothesis test with the data. Gary wants to know whether or not π equals 0.22, and suspects that it may actually be different from than 0.22. Gary randomly selects 130 brick, and 39 of them are non-face (this is a different random sample than Brianna's!).

a. Gary's null hypothesis claims that p:
b. Gary's alternative hypothesis claims that p:

Null hypothesis:  

Alternative hypothesis:  

Step-by-step explanation:

Data given and notation

n=130 represent the random sample taken

X=29 represent the bricks with non face results

estimated proportion of  interest

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

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 equal to 0.22 or not, the system of hypothesis are.:  

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  

Since we have all the info requires we can replace in formula (1) like this:  

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 bilateral test the p value would be: