STAT11-111: Business Statistics Analysis Assessment

Homework Task 2

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 preliminary analysis of university student data, your team are now reviewing engagement and satisfaction metrics.

1. The team finds that the number of hours students spend studying per week is normally distributed, with a mean of 8 hours and a standard deviation of 3 hours and 18 minutes. 

• What is the probability that a student studies for less than 5 hours per week?
• What proportion of students study for at least the recommended 10 hours per week? 
• What percentage of students study for between 7-10 hours per week?
• What is the minimum number of weekly study hours a student must log to be classified among the top 1% of most highly engaged students? 
• What range of study hours corresponds to the middle 50% of students?

2. Student satisfaction ratings are provided below, where 1=Bad, 10=Excellent:

• What is the probability that a student provides an “excellent” rating?
• What is the probability that a student provides a rating of at least 7? 
• Determine the average student satisfaction rating provided. 
• Determine the standard deviation of the rating. 
• Suppose an online university had the same average student satisfaction rating but had a standard deviation of 4.2. Which university received more consistent feedback from students? Briefly explain.

Summary of Assessment Requirements

Assessment Type: Homework Task 2 Problem-based statistical analysis using Microsoft Excel.
Estimated Completion Time: 13 hours.
Objective: To analyze university student engagement and satisfaction metrics using statistical methods, clearly present workings, and interpret results in a practical context.

Key Pointers to Be Covered:

1. Normal Distribution Analysis

   • Calculate probabilities for students studying less than, more than, or between certain weekly hours.
   • Identify top-performing students (top 1%) based on study hours.
   • Determine ranges corresponding to middle 50% of study hours.

2. Student Satisfaction Ratings Analysis

   • Compute probabilities for specific rating outcomes (e.g., “excellent” or ≥7).
   • Calculate average and standard deviation of ratings.
   • Compare consistency of student feedback across universities with different standard deviations.

Tools Required: Microsoft Excel for all calculations and visual presentation of data.

Step-by-Step Approach Guided by Academic Mentor

Step 1: Understanding the Problem and Dataset

The mentor first helped the student review the dataset and clearly understand the questions. They highlighted which statistical techniques were appropriate for each task (e.g., z-scores for normally distributed study hours, probability calculations, descriptive statistics for satisfaction ratings).

Step 2: Normal Distribution Calculations (Study Hours)

• Less than 5 hours: Mentor guided the student to calculate the z-score using z=X−μσz = \frac{X - \mu}{\sigma}z=σX−μ and use Excel’s NORM.S.DIST function to find the probability.
• At least 10 hours: Student learned to calculate the probability of the complementary event using 1 - NORM.S.DIST(z).
• Between 710 hours: Mentor showed how to compute the probability difference between two z-scores.
• Top 1% of students: Student applied the inverse normal function (NORM.INV) to find the minimum threshold for top engagement.
• Middle 50% of students: Mentor explained how to calculate the interquartile range using the 25th and 75th percentiles with Excel formulas.

Step 3: Student Satisfaction Ratings Analysis

• Probability of specific ratings: Student learned to count frequency distributions and convert them to probabilities.
• Probability of rating ≥7: Mentor guided the student to sum probabilities for all ratings ≥7.
• Average and Standard Deviation: Student applied Excel functions AVERAGE and STDEV.P.
• Comparing consistency: Mentor encouraged the student to analyze which standard deviation indicated more consistent feedback and explain the rationale in practical terms.

Step 4: Interpretation of Results

For each calculation, the mentor emphasized writing a clear interpretation in plain language, linking statistical results to practical insights about student engagement and satisfaction.

Outcome Achieved

• The student successfully completed all calculations and presented them clearly in Excel with proper notation.
• Probabilities, averages, and standard deviations were accurately calculated.
• Practical interpretations were included, demonstrating understanding of both statistical methods and their implications for student engagement and feedback.
• The student learned to use Excel effectively for statistical analysis and to communicate results meaningfully.

Learning Objectives Covered

1. Apply statistical techniques (z-scores, normal distribution, probabilities, descriptive statistics) in practical contexts.
2. Use Excel for efficient and accurate statistical calculations.
3. Interpret statistical results and relate them to real-world scenarios (student engagement and satisfaction).
4. Compare datasets using standard deviation to understand variability and consistency.
5. Present findings clearly with appropriate notation and logical reasoning.

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