Question

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
Part 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 α = 0.05 significance level.

Part 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.

Part C: Describe the conclusion about the mean difference between the number of burps that might be drawn from the interval. How does this relate to your conclusion in part A?"

Answer 1

Answer:

This is a special type of data set in that it uses the same subjects to record the number of burps for both the root beer and cola, meaning the data is paired. I would perform a paired t-test to see if there is a difference between the mean number of burps for both types of cola. Your instructions only asked to test for a difference in the number of burps, so the direction of the alternative hypothesis is unknown, making it a two-tailed test. However, the problem stated that "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," and you could use this assumption to test that the mean number of burps while drinking root beer is more than that for cola, giving you a more precise answer versus doing a two-tailed test. Of course, you must designate which sample represents the first mean and which one represents the second mean. See below as an example:

µ1 = mean number of burps while drinking root beer.

µ2 = mean number of burps while drinking cola.

µD = mean of the differences in burping for root beer and cola.

µD = µ1 - µ2

Null hypothesis: there is no difference between the mean number of burps for root beer and cola.

H0: µD = 0

Alternative hypothesis: the mean number of burps while drinking root beer is more than than the mean number of burps while drinking cola.

HA: µD > 0 .

You can use any statistical software to help compute your test, but I recommend Statdisk, because it is free, requires no downloads, and very user-friendly. All you have to do is input your data in columns.

Step-by-step explanation: