Question

For this exercise, you will need to use the packages `mosaic` and `dplyr`.

```{r warning=FALSE, message=FALSE}
# install packages if necessary
if (!require(mosaic)) install.packages(`mosaic`)
if (!require(dplyr)) install.packages(`dplyr`)
# load the package in R
library(mosaic) # load the package mosaic to use its functions
library(dplyr) # load the package dplyr to use data management functions
```

1. For decades it's been suspected that schizophrenia involves anatomical abnormalities in the hippocampus, an area of the brain involved with memory. The following data bearing on this issue are from Suddath et al. (1990) and were used by Ramsey and Schafer (3rd ed., 2013, p. 31. Display 2.2). The researchers obtained MRI measurements of the volume of the left hippocampus from 15 pairs of identical twins discordant for schizophrenia, i.e, one the twin is affected with schizophrenia The data are displayed in the following table.

### Do not delete this code chunk
```{r}
# another way to load a small data set using `read.table()`
schizophrenia <- read.table(header = T, text="
pair affected unaffected
1 1.27 1.94
2 1.63 1.44
3 1.47 1.56
4 1.39 1.58
5 1.93 2.06
6 1.26 1.66
7 1.71 1.75
8 1.67 1.77
9 1.28 1.78
10 1.85 1.92
11 1.02 1.25
12 1.34 1.93
13 2.02 2.04
14 1.59 1.62
15 1.97 2.08
")
is.data.frame(schizophrenia) # check if object `schizophrenia` is a valid data frame
str(schizophrenia)
schizophrenia
```

i. use `mutate()` to create a new variable `diff` which is the difference of the MRI measurements of each pair.
  
ii. use the pipe `%>%` operator add the new variable `diff` as column to `schizophrenia`.
  
iii. use `summarise` to compute the average difference of the MRI measurements. Use the pipe `%>%` operator to string multiple functions.
  
iv. use `summarise` to compute the standard deviation of the difference of the MRI measurements. Use the pipe `%>%` operator to string multiple functions.
  
v. based on your answers in (iii) and (iv), do you think there is evidence in favor of the initial hypothesis there is difference in the MRI measurements of the volume of the left hippocampus between those affected and unaffected with schizophrenia?   
  
  
### Code chunk
```{r}
# start your code

# last R code line
```

Answer 1

The code and the results are given below