Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.
As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:
Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Root beer 6 8 7 7 4 2 3 6 3 8 2 1 5 1 3 4 2 4 5 10
Cola 4 5 5 6 2 3 3 5 4 7 4 0 5 3 3 2 1 1 7 7
A) Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola?
Give appropriate statistical evidence to support your response at the 0.05 significance level.
Give appropriate statistical evidence to support your response at the 0.10 significance level.
Compare your findings.
B) How much of a difference is there when an individual burps from drinking root beer than from drinking cola?
Construct and interpret a 95% confidence interval.
Construct and interpret a 90% confidence interval.
Compare your findings.
C) Describe the conclusions about the difference between the mean number of burps that might be drawn from the interval. How do they relate to your conclusion in part A?