The average amount of caffeine in a 12-oz serving of Coke is 35 mg

The average amount of caffeine in a 12-oz serving of Coke is 35 mg... if it were to come straight from the factory in Atlanta, GA; however, because soda fountain machines are not always cleaned adequately, the actual amount of caffeine in Coke varies depending on where it is purchased and served. A researcher buys 20 fountain Cokes from 12 different restaurants and records the mean caffeine amount for each restaurant. The researcher finds that the average amounts of caffeine in the Cokes served at McDonald’s, Burger King, and Five Guys are 35.5 mg, 37 mg, and 42 mg, respectively.

1. Imagine that the researcher conducted three separate t-tests comparing the Cokes at McDonald’s, Burger King, and Five Guys (in that order) with the average of 35 mg. Assume that the standard deviation of each sample was identical. Would the absolute values of the t-tests get smaller, bigger, or stay the same? How do you know? Be sure to define what a t-score tells you.

2. Would the p-values associated with the above t-tests get smaller, bigger, or stay the same? How do you know? Be sure to define what a p-value tells you.

3.The figure to the right shows more data from the previous experiment. Each bar represents the mean caffeine of Coke, and the error bars represent 95% confidence intervals. Use it to answer the questions below. 

Why does the first bar not have error bars?

4. Which sample(s) is (are) significantly different from the population?

5.Rank Arby’s, Burgerville, and Taco Time in order from biggest p-value to smallest p-value and explain your answer in one sentence.

6. A man with psychic powers tells you that one of the above three tests is associated with a Type I error. Which example do you think is associated with a Type I error, and how do you know?