The effect of coffee consumption

Task 4
Data Description
The dataset given here shows the effect of coffee consumption on the test scores of
University students.
Sub setting the Data
Initially the data had 685 records out of which 131 had missing values. For that reason, a
subset is formed by omitting the missing values that contains 554 observations.
Objective of the Study
The main objective is to investigate whether ingestion of coffee has effect on the marks
of University students. To achieve this, at first it is checked if there is any notable variation in
scores due to coffee intakes. Further, the relation between age of a student and test score after
having coffee is also visualized.
Descriptive Statistics
Here Gender is a categorical variable with 1=male and 2=female. A descriptive study is
performed for the rest of the numerical variables (McCormick and Salcedo 2017).

It can be noted that the average age of a stude4nt is 25.62≈26 years. 50% students have
age less than 26 years. Further, 25% students are below 22 years and 25% are above 29 years
(from the percentiles). Highest number of students are 20 years old. The value of skewness show
that the data is positively skewed.
The average mark (55.37 approx. before) is increased after consuming coffee (70.32=70
approx.). From the medians, it can be said that 50% students scored less than 60 in test 1 and 73
that for test 2. In test 1, highest number of students got 62 highset frequency of score is 75 is test
2. Both the variables have negative skewness. Hence, they have distributions skewed to the left.
Normality Test
The normality assumptions are checked using histogram and normal Q-Q plot (Das and
Imon 2016).

The histograms imply that the test 1 scores are approximately normally distributed
irrespective of gender.

The data points are very close to the normal line in both graph 3 and 4. Hence normality
assumption is satisfied.

Graph 5 and 6 show that the data is distributed normally for both male and female
students (Hinton, McMurray and Brownlow 2014). Moreover the normal plots also show that the
data points are very close to the normal line. Hence the normality assumption is fulfilled.
Since the data follow normality, parametric tests can be performed.

Research Hypothesis
The research hypothesis can be taken as-
There is no significant influence of coffee consumption on the scores of students.
Part 1: Observing the relation between two test scores
For this part, the null hypothesis can be written as-
There is no significant difference in test scores after coffee intakes.
The alternate hypothesis assumes that there is notable variation between test 1 and test 2
scores.
Since the before and after test results are recorded for the same students, a paired t-test would be
perfect for testing the hypothesis (Ross and Willson 2017). The relevant outputs are given below.

The correlation coefficient from tables 2 is found to be 0.972 which is quite high. Hence,
it can be deduced that the test1 and test 2 scores have a strong positive linear relationship.
From table 3, the t-statistic is obtained as 140.874 with d.f 553 which is significant at 5%
level. Hence the null hypothesis is rejected and based on the data, it can be concluded that there
is significant difference in test scores before and after consumption of coffee (Lowry 2014).
Part 2: Association between age and test 2 scores
In this case, the testing hypotheses are:
Null Hypothesis: There is no correlation between age and scores after coffee intakes.
Alternative Hypothesis: There is significant correlation between age of a student and his score
after coffee intake.
Pearson’s correlation coefficient is the most suitable tool for this purpose (Schober, Boer
and Schwarte 2018). The outputs are shown below.

The correlation coefficient is found to be -.131 which is significant at 1% level. Hence
the null hypothesis is rejected and the alternate one is accepted. Further, the negative correlation
shows that an older student gets less marks in the test after coffee intakes.
Exploration of the research objective
From the descriptive study, it can be observed that the average marks have been
increased due to coffee intakes. Further, the paired t-test implies that the marks obtained after
coffee consumption is significantly different than the marks obtained before. Hence, it is inferred
that coffee intakes have notable influence on the test scores of University students.

References
Das, K.R. and Imon, A.H.M.R., 2016. A brief review of tests for normality. American Journal of
Theoretical and Applied Statistics, 5(1), pp.5-12.
Hinton, P.R., McMurray, I. and Brownlow, C., 2014. SPSS explained. Routledge.
Lowry, R., 2014. Concepts and applications of inferential statistics.
McCormick, K. and Salcedo, J., 2017. SPSS statistics for data analysis and visualization. John
Wiley & Sons.
Ross, A. and Willson, V.L., 2017. Paired samples T-test. In Basic and advanced statistical
tests (pp. 17-19). Brill Sense.
Schober, P., Boer, C. and Schwarte, L.A., 2018. Correlation coefficients: appropriate use and
interpretation. Anesthesia & Analgesia, 126(5), pp.1763-1768.