Question

In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work (University of Central Florida Undergraduate Research Journal, Spring 2005): $$ \begin{array}{cccc} & \begin{array}{c} \text { Sample } \\ \text { Size } \end{array} & \begin{array}{c} \text { Mean } \\ \text { GPA } \end{array} & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} \\ \begin{array}{c} \text { Students Who Are } \\ \text { Employed } \end{array} & 184 & 3.12 & 0.485 \\ \begin{array}{c} \text { Students Who Are } \\ \text { Not Employed } \end{array} & 114 & 3.23 & 0.524 \\ & & & \end{array} $$ The samples were selected at random from working and nonworking students at the University of Central Florida. Estimate the difference in mean GPA for students at this university who are employed and students who are not employed.

Short answer

The difference in the mean GPA for students who are employed and those who are not is -0.11.

Step-by-step solution

Identify the Means

From the given data, it can be seen that the Mean GPA of students who are employed (Mean1) is 3.12 and the Mean GPA of students who are not employed (Mean2) is 3.23.

Calculate the Difference in Means

Subtract Mean2 from Mean1 using the formula \(difference = Mean1 - Mean2\). This will give the difference in Mean GPA of the two groups.

Evaluate the Mean Difference

Subtract \(3.23 (Mean2)\) from \(3.12 (Mean1)\) to get the difference. The difference would be \(3.12 - 3.23 = -0.11\). Therefore, the mean GPA of employed students is 0.11 lower than that of non employed students.

Key concepts

Mean GPA Comparison

When it comes to academic achievement, Grade Point Average (GPA) is a pivotal metric used to assess student performance. Comparing mean GPAs can provide valuable insights into the academic effects of various factors, such as employment status.In the case of the study from the University of Central Florida, researchers aimed to identify any differences in the academic performances between employed and non-employed students by comparing their mean GPAs. The mean GPA is essentially the average score of a group's academic grades, which is calculated by adding all the individual GPAs and dividing by the number of students. Here, employed students had a mean GPA of 3.12, while non-employed students had a slightly higher mean GPA of 3.23.

To determine the impact of employment on academic performance, the difference between these two means was calculated, which revealed that students who were employed had, on average, a 0.11-point lower GPA than their non-employed counterparts. This negative difference suggests that employment might be associated with a slight decline in academic performance. However, it's crucial to consider other possible factors and to understand that correlation does not imply causation without further research.

Standard Deviation

Let's delve into the concept of standard deviation, an essential statistic that measures how spread out the numbers in a data set are. In a real-world scenario like evaluating student GPAs, standard deviation offers insight into the variability of students' grades within each group.Considering our study, the standard deviation for the GPA of employed students was 0.485, whereas the standard deviation for non-employed students was 0.524. These figures indicate that the GPA scores of non-employed students are slightly more spread out than that of employed students, meaning there's more variability in the GPAs of the non-employed group.

Why is this important?

It allows us the ability to understand not just the average performance of students but also the consistency of their grades. A lower standard deviation suggests that the GPAs are closer to the mean, showing a more consistent academic performance. In contrast, a higher standard deviation indicates more diverse outcomes and hence less predictability. By understanding standard deviation, educators and students alike can get a clearer picture of the overall performance landscape.

Sample Size

When analyzing statistics, the significance of a sample size cannot be overstated. The sample size refers to the number of observations or individuals included in a study. It plays a critical role in the reliability of statistical analyses and the validity of the resulting conclusions. Larger sample sizes generally provide more precise estimates of what researchers aim to measure, reducing the margin of error and increasing the confidence in the findings.In the study comparing the GPAs of employed versus non-employed students, the sample sizes were 184 and 114, respectively. The sample size impacts the weight of the evidence provided by the study outcomes. Larger samples are typically better representations of the entire population and are less susceptible to random errors or anomalies.

What does this mean for the study?

Although both sample sizes are relatively modest, the differing sizes could introduce an element of bias or affect the precision of the GPA comparison. Ideally, for robust conclusions, similar sample sizes are preferred, as they ensure a balanced comparison between groups. Nonetheless, the provided sample sizes can still offer important preliminary insights into the relationship between employment and academic performance.