Water Taste Test

Students & faculty at Longwood University conducted a blind taste test to investigate whether people prefer one type of bottle (or tap) water more than another. The results came from a convenience sample of 109 people attending an Oktoberfest celebration on campus. Subjects were presented with four identical cups of water and were asked to identify which cup tasted the best. The results, separated by gender, are shown in the two way table below.

water = read.csv("http://people.hsc.edu/faculty-staff/blins/classes/spring18/math222/examples/water.csv")
water.table = table(water)
water.table

##               Gender
## Preference      Female  Male
##   Aquafina          17    10
##   Fiji              33    11
##   Sam's Choice      19     7
##   Tap Water          8     4

Exercise 1

Ignoring gender, does it appear that the type of water matters? To answer this question, you can use the one-way table:

preference.table = table(water$Preference)
preference.table

## 
##     Aquafina         Fiji Sam's Choice    Tap Water 
##           27           44           26           12

Exercise 2

What if we remove tap water from the sample and focus on the three types of bottled water? Do people have real preferences about bottled water or could these differences just be random? Use the data table below.

bottle.table = preference.table[-4] # This command removes the 4th entry from preference.table

Exercise 3

Use a permutation test to determine is there is a significant difference between the preferences of men vs. women. Why might a permutation test be better than a chi-squared test for association?