STAT11-111: Business Statistics Lead Educator Analysis Assessemnt

Homework Task 3

Task Description

Homework tasks consist of problem-based questions. Students are required to perform all statistical analysis using tools in Microsoft Excel. Working must be presented clearly, using appropriate statistical notation and techniques studied in class, and all results must be interpreted in a practical context. It is estimated that this homework task should take approximately 1-3 hours to complete.

Questions

Following your earlier analysis of University X’s student data, your team are now reviewing the impact of a recently launched student wellbeing program. University management wants to evaluate whether the new program has led to a measurable impact on student engagement and student satisfaction.

Historically, 72% of students reported being satisfied with their university experience. After introducing the wellbeing program, a survey of 200 students found that 150 were satisfied and the average Engagement Index was 67.5 with a standard deviation of 13.4.

1. Using a 5% level of significance, test whether the introduction of the student wellbeing program has improved overall student satisfaction.
2. The Engagement Index, measured as a composite score from LMS activity, tutorial participation and student event attendance, was 61 before the introduction of the wellbeing program. Can you conclude whether there has been a significant difference following the launch of the wellbeing program? 
3. Suppose a second (interstate) university introduced a similar wellbeing program and found that 116 out of 160 students were satisfied. At the 10% level of significance, test whether student satisfaction is higher at University X.
4. Using concepts covered in class, comment on the reliability of your above conclusions. 
5. Briefly explain how the results of these tests could inform university decision-making about whether to continue, expand, or adjust the wellbeing program. 

Summary of the Assessment Requirements

This homework task requires students to complete a set of problem-based statistical questions, using Microsoft Excel to perform all calculations and present workings clearly. The assessment focuses on applying statistical techniques learned in class to evaluate the effectiveness of a newly introduced student wellbeing program at University X.

Students are expected to:

1. Conduct a hypothesis test for a population proportion
   Determine whether student satisfaction has improved compared to the historical rate of 72%.
   Use a 5% significance level and interpret the results in context.
2. Conduct a hypothesis test for a population mean
   Compare the post-program Engagement Index (mean = 67.5, SD = 13.4, n = 200) with the previous index of 61.
   Assess whether the difference is statistically significant.
3. Compare two population proportions
   Test whether student satisfaction at University X is higher than at a second interstate university (116/160 satisfied) at a 10% significance level.
4. Comment on the reliability of the conclusions
   Discuss sampling limitations, variability, assumptions of hypothesis testing and real-world factors.
5. Explain practical implications for university decision-making
   Use the statistical outcomes to advise whether the wellbeing program should be continued, revised, or expanded.

All results must be presented with correct statistical notation, appropriate interpretation, and contextual explanation.

How the Academic Mentor Guided the Student 

Step 1: Interpreting the Task and Structuring the Solution

The mentor helped the student break the task into five clear statistical problems.
They reinforced that the work should follow a logical structure:

• Identify the appropriate statistical test
• Define hypotheses
• Perform calculations using Excel
• State test statistic, p-value, or critical value
• Interpret in a real-world context

This structure ensured clarity and alignment with classroom expectations.

Step 2: Testing Improvement in Student Satisfaction (Proportion Test)

The mentor guided the student to:

• Recognize it as a one-tailed hypothesis test for a single population proportion.
• Set up:
  • H₀: p = 0.72
  • H₁: p > 0.72
• Use Excel formulas to compute sample proportion, standard error, z-score, and p-value.
• Interpret whether the program significantly improved satisfaction at the 5% level.

Step 3: Testing the Engagement Index Change (Mean Test)

The mentor explained:

• This requires a one-sample z-test for the mean, since population SD is unknown but sample size is large.
• Formulate hypotheses:
  • H₀: μ = 61
  • H₁: μ ≠ 61
• Use Excel to compute z = (sample mean − historical mean) / (SD / √n).
• Interpret whether engagement significantly increased.

Step 4: Comparing Two Universities (Two-Proportion Test)

The mentor instructed the student to:

• Treat the comparison as a two-proportion z-test at a 10% significance level.
• Set up:
  • H₀: p₁ ≤ p₂
  • H₁: p₁ > p₂
• Use Excel to calculate pooled standard error, test statistic, and p-value.

Step 5: Assessing Reliability of Results

The mentor guided the student in commenting on:

• Whether the sample sizes were sufficient
• Whether assumptions of normal approximation hold
• Possible biases (survey design, program duration, student demographics)
• Real-world variability beyond statistical significance

This helped the student move beyond numbers toward critical interpretation.

Step 6: Explaining Decision-Making Implications

The mentor encouraged the student to connect statistical findings to practical choices:

• If satisfaction and engagement significantly increased → consider expanding the program
• If results were mixed → refine program elements
• If no significant improvement → review effectiveness before further investment
• Highlight the importance of continuous data monitoring

This step ensured the student demonstrated application-oriented thinking.

Final Outcome and Learning Objectives Achieved

Outcome

The student produced a structured statistical analysis that:

• Correctly applied proportion and mean hypothesis tests
• Used Excel effectively for calculations
• Interpreted results in the context of student wellbeing
• Provided well-reasoned commentary and recommendations

Learning Objectives Achieved

• Application of hypothesis testing concepts (proportion tests, mean tests, two-sample tests)
• Use of Excel for statistical calculations
• Clear use of statistical notation and step-by-step methodology
• Critical thinking about data reliability and real-world variability
• Ability to link statistical results to decision-making in an organisational context

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