University Statistics Assignment: Correlation and Random Sampling

This assignment examines the concept of correlation coefficients, specifically focusing on a scenario where the correlation between income and happiness is analyzed. The student is tasked with interpreting a correlation coefficient of +0.25, indicating a weak positive correlation, and explaining its implications. The assignment further explores the impact of increasing the sample size to one thousand subjects, predicting that the correlation would likely move closer to zero and the confidence interval would increase, due to the increased density of data points and the coefficient's fluctuation toward the population's true value. The importance of random sampling is emphasized, with a detailed explanation of its role in ensuring accurate representation and minimizing bias, supported by an example of a survey to determine the number of right-handed students in a secondary school. The assignment uses statistical analysis, including the Pearson correlation coefficient, and references relevant academic sources.

You are interested in knowing whether wealthier people are happier. You collected data
from fifty people about their incomes and their overall happiness levels on a scale of 1 to
10. Upon analyzing the results, you find that the correlation coefficient has a value of?0.25.
On the basis of this data, respond to the following:
• How would you interpret the correlation coefficient in terms of strength and direction?
Correlation coefficient is a statistical analysis that is used in indicating the association between
dependent variable and independent variable. Therefore, the correlation of +0.2 indicates weak
correlation between peoples income independent variable and happiness level dependent level
(Adler and Parmryd, 2010).
According to this information, there would be a low association between one’s income
increasing and there increase in happiness. Therefore only 20% portion of happiness would be
covered incase one’s income is increased.
• How would the results be affected if you increased the number of subjects in the study to
one thousand?
Increasing the number of subject samples would increase the density of the scatter point on a
scatter diagram, it would also increase the mean of the observations determined. Increasing the
subject samples size, the confident interval would be high while the correlation would move
close to zero.
As the subject sample goes up, the coefficient of correlation would fluctuate at less strength
towards the true value for the population.
Why might that affect the overall correlation?
There would be a further weak linear relationship between income independent variable and
happiness dependent variable when the number of subject would be increased fifty people to one
thousand people. The correlation coefficient would tend to move close to zero. Correlations that
are obtained on small subject samples would produce realistic large correlation coefficient as
compared to large subject samples.
• How important is it to randomly select subjects? Explain in detail using an example of a
sample that might not be truly representative of the population.
Random samplings are important concepts in the jurisdiction of research statistical methods.
Random sampling would therefore mean a method that would be used to select an individual
from a population to be involved in study research. Therefore, this would mean that samples

would be randomly selected from population data to fully participate on the research study. The
method involves a part of samples to act as a preventative of the larger data population. It would
be important to that samples would only be regarded as random if all the individual data have
equal or same probability chance of being selected from the population data (Henry and
Temtime, 2010).
Random sampling selection generally would allow accurately representation and easy to use. The
method is easier to extract samples of research from larger samples of populations. Random
selection only depends on randomness and would not be governed by subdivision of populations.
Selection of sample subject at random from populations that are large would yield representative
samples from the groups that would be under study. The accuracy of random sampling and its
simplicity would give a high priority of it being considered in analyzing large samples of
population. It also represents the population that would be targeted at and a high chance
eliminates sampling bias.
Randomly selecting subjects would allow room for error that would be represented by a minus
and a plus variance.
Example
In a secondary school survey that was taken to determine how many students would be right-
handed, a randomly selected sampling would determine that 8 out of hundred sampled were
right-handed. The conclusion made was 8% of the population of students of secondary school
was right handed. Where the fact remains that the average global was close to 10%.
References
Adler, J., & Parmryd, I. (2010). Quantifying colocalization by correlation: the Pearson
correlation coefficient is superior to the Mander's overlap coefficient. Cytometry Part
A, 77(8), 733-742..
Cameron, A. C., & Trivedi, P. K. (2010). Microeconometrics using stata (Vol. 2). College
Station, TX: Stata press.
Henry, O. and Temtime, Z., 2010. Recruitment and selection practices in SMEs: Empirical
evidence from a developing country perspective. Advances in Management.