Jerry's Fish Shack claims that 16% of its employees are late to work once a week. The manager surveyed 25 employees and found that actually 20% are late to work once a week. What does the test statistic calculation look like in this situation for an appropriate hypothesis test?

We need to conduct a hypothesis in order to test the claim that the true proportion of employess are late to work is 0.16, so we need to apply a one sample proportion test:  

Null hypothesis:  

Alternative hypothesis:  

Step-by-step explanation:

Data given and notation

n=25 represent the random sample taken

estimated proportion  

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 of employess are late to work is 0.16, so we need to apply a one sample proportion test:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, 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: