Question

The manufacturer of Twitchy Energy Drink is doing a quality inspection to make sure that the caffeine content of the drink is meeting specifications of 79.9 mg per can. Suppose a quality inspector takes a sample of size 13 from the production line and finds that the average caffeine content in the sample is 78.3 mg, with a standard deviation of 0.25 mg.

Calculate the test statistic for testing the hypothesis that the true mean caffeine content is less than 79.9 mg per can. Report your answer to two decimal places.

Answer 1

sample std dev ,    s =    0.2500                  
Sample Size ,   n =    13                  
Sample Mean,    x̅ =   78.3000                  
                          
  
Standard Error , SE = s/√n =   0.2500   / √    13   =   0.0693      
t-test statistic= (x̅ - µ )/SE = (   78.300   -   79.9   ) /    0.0693   =   -23.08