Researchers equiped male and female college students with a small device that secretly recorded sounds for a random 30 seconds during each 12.5 minute period over 2 days. By counting the words each subject spoke while being recorded, the researchers were able to estimate how many words each subject spoke per day. The results are contain in the following file.
talking = read.csv("http://people.hsc.edu/faculty-staff/blins/classes/spring18/math222/examples/talking.csv")
men = subset(talking,Sex=="M")$Words
women = subset(talking,Sex=="F")$Words
summary(talking)
## Sex Words
## F:27 Min. : 1537
## M:20 1st Qu.: 8892
## Median :12584
## Mean :14658
## 3rd Qu.:19186
## Max. :39681
sd(men)
## [1] 8342.472
summary(men)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3998 7868 10770 12870 13870 37790
sd(women)
## [1] 8421.497
summary(women)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1537 9915 13620 15980 21420 39680
In this sample there were 20 men and 27 women. Here is a side-by-side boxplot showing the differences between the two groups.
boxplot(men,women,names = c("Men","Women"),horizontal = T,col='gray',xlab="# Words per Day")
One natural question to ask is: does this data give statistically significant evidence that there is a difference between the number of words spoken by men versus women? For each of the following statistical tests, describe whether it is a valid option for answering this question and comment on any advantages or disadvantages it has compared with the other options.
A second natural question is: how big is the difference between the two genders? Once again, comment on these options for answering this question.