In: Statistics and Probability
Over the last 20 years, the number of students who hold a job while attending university fulltime has increased. Work responsibilities may ‘compete’ for time and energy with course responsibilities, and consequently, may affect student academic success. An educational researcher is interested in determining whether student employment influences academic success. The research has obtained a relevant sample of university students, and has determined the following information for each student:
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In our lecture on Planning Ahead: Sampling variability, you were introduced to a set of five (5) questions that can be used to help decide upon a relevant statistical inference procedure.
my answer to a is:
a) what is your analysis goal?
goal is to determine whether student employment influences academic success.
how many ‘samples’ or groups are you comparing?
Based on the scenario above, the researcher is comparing a single sample of university students and each student in the sample is surveyed. but there are 2 measures for each observation
are the ‘samples’ independent or paired?
the sample is independent as the data is obtained from each student each case is unrelated to the other.
what type of data are you collecting? Quantitative or categorical?
the data being collected quantitative. Both the employment status and their course grades produce a numerical value to describe the data
what parameters are of interest?
the parameters of interest are the mean hours worked per week and the mean of the student’s course grades. the correlation between the 2 is also important as it tells us about the relation between hours worked per week and student's course grades. (scatter plot may give us a rough idea of kind of relationship)
b) the inference procedures that can be used here is regression analysis.
Statistical relation may be expressed as
Y: student's course grades, X: Hours worked per week
We check if = 0 or not using t test to conduct hypothesis tests on the regression coefficients obtained in simple linear regression. that is if the hours worked per week and the student’s course grades have significant relation or not.
c) the test statistic used here is
where is the least square estimate of slope given by Sxy/Sxx
= standard error of given by,
Tcal ~ t distribution with n-2 degree of freedom