Question

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: their employment status (specifically, the typical number of hours worked per week during the school term) their course grades for the most recent school term (specifically, their mean grade (%) across all their courses during the school term).

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.

1. Identify each of the five (5) questions and answer each question based on the scenario described above.
2. Based on your answers to part a, identify which of the inference procedures covered in class is most appropriate to analyse the researcher’s data?
3. Assume the researchers for the above scenario have obtained relevant simple random sample(s). Identify (by name) the sampling distribution that underlies the statistical inference procedure named in part b. Then, give the formulae for the mean and standard deviation for the sampling distribution you have identified.

my answer to a is:

1. The first question is “what is your analysis goal?”. The analysis goal based on the scenario above is to determine if student employment has an influence on their academic success. The second question is “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. The third question is “are you ‘samples’ independent or paired?”. In this scenario, the sample is independent as the data is obtained from each student each case is unrelated to the other. The fourth question is “what type of data are you collecting? Quantitative or categorical?”. Based on the scenario above, the data being collected quantitative. Both the employment status and their course grades produce a numerical value to describe the dat The last question is “what parameters are of interest?”. In the above scenario, the parameters of interest are the hours worked per week and the mean of the student’s course grades.

Answer 1

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