LFIAL2260 Resit Exam 2024
Mejia Vargas Gabriel Alfonso
2024-08-23
Total: 40 points
Instructions:
1. Rename this file by replacing “LASTNAME” with your last name. This
can be done via the RStudio menu (File >> Rename).
2. Write your full name in the chunk above beside
author:.
3. Before beginning, it is good practice to create a directory that
contains your R scripts as well as any data you will need. This can be
done in the console directly with the setwd() function or
via the RStudio menu (Session >> Set Working Directory).
4. Write R code to answer the questions below. The code should be
written within the chunks provided for each question. These chunks begin
with three back ticks and the letter r in curly brackets
(```{r}) and end with three back ticks. You can add as much
space as you need within the chunks but do not delete the back ticks or
otherwise modify the chunks in any way or the file will cause errors
when compiled.
5. When you have answered all of the questions, click the
Knit button. This will create an HTML file in your working
directory.
6. Upload the HTML file to Moodle.
Data description:
The stay-abroad.csv data set contains fictional data from
British students studying French at university. A subset of the British
students participated in a year abroad to France during their studies.
Specifically, they could go to France for a year to do either an
internship at a French company, an erasmus exchange at a French
university, or a language assistantship, where they would teach English
to French high school students. In addition to the stay abroad, the
British students could also choose to participate in book club, where
they would read and discuss French books. At the end of their studies,
each student wrote one short argumentative essay and took a vocabulary
test. The variables are described below:
ID: anonymous ID corresponding to the student who wrote the argumentative essay and took the vocabulary test
ABROAD: whether the student participated in a stay abroad in France
BOOKCLUB: whether the student participated in a voluntary French book club
PLACEMENT: the type of stay of the student in their year abroad.
LEX.SOPH: a measure of lexical sophisticationECON.VOCAB: the sophistication of “economics-related” vocabulary in the text
VOCAB.TEST: the score on the vocabulary test
Hint:
While completing the exam, it may be helpful to keep the following
questions in mind:
- What kinds of variables are involved in your hypothesis (integer,
ordinal, categorical etc.) and how many?
- Are data points in your data related such that you can associate
them to each other in a meaningful way?
- What is the statistic of the dependent variable in the statistical
hypothesis?
- What does the distribution of the data of your test statistic look
like?
- How big are the samples you collected?
- What assumptions must be met before running a particular statistical test?
1 General Questions (Total: 5 points)
1.1 Load any packages you
will need and then load the data set (stay-abroad.csv) into
a dataframe called “sa”. 1 point
setwd("~/Desktop/Statistics Exam")
library (readxl)
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ readr 2.1.4
## ✔ lubridate 1.9.3 ✔ stringr 1.5.0
## ✔ purrr 1.0.2 ✔ tibble 3.2.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(car)## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:purrr':
##
## some
##
## The following object is masked from 'package:dplyr':
##
## recodesa<- read.csv("stay-abroad.csv", header = TRUE, stringsAsFactors = TRUE)
attach(sa)1.2 Print an overview of
the data frame to check if all variables have been imported properly.
What type of variable is PLACEMENT? 1 point
str(sa)## 'data.frame': 169 obs. of 7 variables:
## $ ID : Factor w/ 169 levels "S101","S102",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ ABROAD : Factor w/ 2 levels "no","yes": 1 2 2 2 1 2 2 1 2 2 ...
## $ BOOKCLUB : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
## $ PLACEMENT : Factor w/ 3 levels "business","erasmus",..: NA 2 1 2 NA 3 1 NA 3 1 ...
## $ LEX.SOPH : num 0.714 2.488 0.97 1.717 1.123 ...
## $ ECON.VOCAB: num 245 274 215 325 245 ...
## $ VOCAB.TEST: num 87.7 86 80.6 67.6 44.3 ...Answer: Placement corresponds to a categorical variable
1.3 Print a summary of the data frame. How many students participated in the book club? 1 point
summary(sa)## ID ABROAD BOOKCLUB PLACEMENT LEX.SOPH
## S101 : 1 no :91 no :141 business :24 Min. :0.7144
## S102 : 1 yes:78 yes: 28 erasmus :27 1st Qu.:1.8628
## S103 : 1 lang_assist:27 Median :2.6117
## S104 : 1 NA's :91 Mean :2.5689
## S105 : 1 3rd Qu.:3.2213
## S106 : 1 Max. :4.8240
## (Other):163
## ECON.VOCAB VOCAB.TEST
## Min. :159.4 Min. :25.61
## 1st Qu.:245.5 1st Qu.:59.07
## Median :275.2 Median :71.33
## Mean :276.4 Mean :70.06
## 3rd Qu.:303.9 3rd Qu.:81.32
## Max. :420.8 Max. :99.54
## Answer: according to the information collected from the data only 28 students participated in the book club.
1.4 Which students received a score greater than 98 on the vocabulary test? 1 point
higher_scorev <- filter(sa, VOCAB.TEST >= 98)
View(higher_scorev)1.5 Print all the data for those students only. Which of those students did not participate in the stay abroad? 1 point
print(higher_scorev)## ID ABROAD BOOKCLUB PLACEMENT LEX.SOPH ECON.VOCAB VOCAB.TEST
## 1 S111 yes no lang_assist 1.643452 303.9004 99.24295
## 2 S122 yes no lang_assist 1.723281 275.1969 99.28448
## 3 S222 no no <NA> 3.214286 253.2977 99.36443
## 4 S230 no no <NA> 3.158168 219.6031 99.54392Answer: according to the data filtered we can see that only two students (S222 and S230) that obtaianed a score greater than 98 did not participate in the stay abroad.
2 You want to test whether learners who participated in a stay abroad (ABROAD = yes) were also more likely to participate in the book club (BOOKCLUB = yes) as compared to learners who did not participate in the stay abroad (ABROAD = no). (Total: 7 points)
2.1 Formulate hypotheses. 1 point
Answer: H0= Students who did not participate in the stay abroad were as eager to join the book club as their counterparts who participated in the stay abroad H1= Students who did not participate in the stay abroad were not as eager to join the book club as their counterparts who participated in the stay abroad
2.2 Summarize the data numerically and represent the data graphically. 2 points
sa_abroad_book <- table(ABROAD,BOOKCLUB)
View(sa_abroad_book)
plot(sa_abroad_book)
2.3 Test your hypothesis with analytical statistics and calculate an effect size if the test is significant. 2 points
2.4 Summarize the result(s). 2 points
Answer:
3 A literature review indicates that reading has a positive impact on vocabulary. You therefore want to test whether students who participated in the book club (BOOKCLUB = “yes”) used a more sophisticated vocabulary (LEX.SOPH) as compared to students who did not participate in the book club (BOOKCLUB = “no”). (Total: 10 points)
3.1 Formulate hypotheses. 1 point
Answer: H0 = Students who participated in the book club do not use more sophisticated vocabulary in comparison to those students that did not participate in the book club H1= Students who participated in the book club use more sophisticated vocabulary in comparison to those students that did not participate in the book club
3.2 Is your alternative hypothesis one-tailed or two-tailed? Explain. 1 point
Answer: the alternate hypothesis is one-tailed provided that that a higher level of sophistication is expected from the students that were part of book club.
3.3 Are the samples dependent or independent? Explain. 1 point
Answer: the samples collected are independent provided that the population studied are students that had different experiences in their learning, therefore, despite the fact that they may belong to the same university, they are considered independent from each other.
3.4 Calculate descriptive statistics and represent the data graphically. 2 points
BookVSVoc <- table(BOOKCLUB, LEX.SOPH)
summary(BookVSVoc)## Number of cases in table: 169
## Number of factors: 2
## Test for independence of all factors:
## Chisq = 169, df = 164, p-value = 0.3783
## Chi-squared approximation may be incorrect3.5 Test your hypothesis with analytical statistics and calculate an effect size if the test is significant. 3 points
NSL.aov <- aov(BOOKCLUB ~ LEX.SOPH, data = sa)## Warning in model.response(mf, "numeric"): using type = "numeric" with a factor
## response will be ignored## Warning in Ops.factor(y, z$residuals): '-' not meaningful for factors3.6 Summarize the result(s). 2 points
Answer: