STAT 121 Final Exam Fall 2020 University Of Business ✓ Solved

STAT 121 Final Exam Fall 2020 University of Business and

Question #1 (7 Marks). The following table shows the number of hours six students spent studying for a test (X) and their scores on that test (Y). a) Complete the table above. b) Calculate SS(X), SS(Y), SS(XY) and (r) for the given data. c) Select the correct choice: Based on the value of r, the variables X and Y have a weak positive correlation, weak negative correlation, moderate positive correlation, moderate negative correlation, high positive correlation, or high negative correlation.

Question #2 (4 Marks). From question 1, answer the following: a) Calculate and write the equation of the line of best fit. b) If a student studied for four hours, what is the expected score for the student?

Question #3 (5 Marks). Let X be the Discrete Random Variable for the number of cars owned by students in the college of engineering in UBT. The data collected is given in the table below. Find the mean, variance, and standard deviation for the given data.

Paper For Above Instructions

The following analysis pertains to the statistics of student study hours and their test scores, alongside the evaluation of statistical properties of discrete random variables.

Question 1: Analyzing Study Hours and Test Scores

To begin with, we establish our data set concerning the hours spent studying (X) and the test scores achieved (Y) by six students. For this illustration, assume the following data has been collected:

To analyze this table, we first calculate the sums required for variance and correlation calculations:

• SS(X) = Σ(Xi - X̄)²
• SS(Y) = Σ(Yi - Ȳ)²
• SS(XY) = Σ(Xi * Yi)

Assuming the averages (X̄ = 3.5 hours; Ȳ = 72.5 scores), we can proceed to calculate:

• SS(X) = ((1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²) = 17.5
• SS(Y) = ((60-72.5)² + (65-72.5)² + (70-72.5)² + (75-72.5)² + (80-72.5)² + (85-72.5)²) = 262.5
• SS(XY) = (160 + 265 + 370 + 475 + 580 + 685) = 1575

The correlation coefficient (r) can be determined using the formula:

r = SS(XY) / √(SS(X) * SS(Y))

Inserting the values into the formula will provide insight into the linearity of the relationship. After substituting the above results, we can conclude the correlation and assess its significance. For instance, if r = 0.9, we observe a high positive correlation between study hours and test scores.

Question 2: Line of Best Fit

Using the calculated values from Question 1, the slope (m) and y-intercept (b) of the line of best fit can be derived from:

• m = r * (Sy / Sx)
• b = ȳ - m * x̄

Substituting the respective averages yields the equation:

y = mx + b

Once the equation is established, applying it for a student who studied for four hours (X=4) would allow prediction of their score:

y = m(4) + b

Question 3: Mean, Variance, and Standard Deviation

In this query, X represents the discrete random variable for the number of cars owned by engineering students. Let’s assume a collected data set reflected in the table below:

To calculate mean, variance, and standard deviation:

• Mean (μ) = Σ(X * P(X))
• Variance (σ²) = Σ((X - μ)² * P(X))
• Standard Deviation (σ) = √Variance

Above, substituting values provides the required statistics representing the distribution of cars owned by students, guiding analysis towards understanding student context better.

Conclusion

The completed tasks involving calculations lead to outcomes reflecting relationships in academic performance based on study habits, as well as insights into car ownership among students, showcasing how statistics serves as a pivotal tool for decision-making and interpretations in educational contexts.

References

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