Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test

Step-by-step explanation:

Information given

represent the sample mean for the content of active ingredient

represent the sample standard deviation for the sample  

sample size  

represent the value that we want to test

t would represent the statistic

represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for the active agent is at least 20 mg, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic would be:

 (1)  

Now we can calculate the statistic:

P value

The degrees of freedom are calculated like this:

Since is a one left tailed test the p value would be: