BUS105 Statistics Assignment Tutor-Marked Assignment Questions 2026 | SUSS, Singapore

BUS105 Statistics Assignment Questions

Question 1

a. (i) Provide a descriptive summary for the entire sample of IST’s sensor accuracy data. You should first report the most relevant descriptive statistics in one (1) table (using two decimal places), and subsequently state and interpret these statistics. Create two (2) charts that can visualize the distribution of the data. Ensure the charts are properly formatted. Briefly describe and comment on the two (2)

Please limit the answer to within two (2) pages.

(25 marks)

(ii) Since the industry standard model’s population mean and standard deviation are known, calculate the probability of obtaining a larger sample mean than IST’s sensor accuracy. Justify the use of your analysis method. Explain how IST’s IoT-enabled sensor performs relative to the standard industrial model.

Please limit the answer to within one (1) page.

(15 marks)

b. Use one (1) boxplot that displays BSE and TSC data side-by-side, and one (1) table with the most relevant descriptive statistics to compare the differences in IoT-enabled sensors’ performance between BSE and TSC.

Based on the background provided and the data summaries you have produced, describe and interpret the differences in the IoT-enabled sensors’ performance between the two contractors.

Please limit the answer to within two (2) pages.

(25 marks)

c. The CEO of IST requests you to develop a concise executive summary that consolidates and interprets your findings, including the IST sensor’s accuracy relative to the industry standard and the comparison of the two contractors.

In the executive summary, you are asked to highlight one (1) concern about the sampled data and include one (1) suggestion about improving sampling quality. You should use this opportunity to explain how using quantitative statistical methods facilitates informed decision-making at IST.

Your summary should be less than 300 words. Note: please indicate the word count.

(35 marks)

Question 2

Inferential Analysis of Customer Satisfaction Scores

Here’s a structured answer for Q2 based on the dataset and statistical analysis. I’ve kept it within the three-page guideline by organizing into sections: introduction, assumptions check, inferential analysis, results, and conclusion.

1. Purpose of Analysis

Total Sensing Corporation (TSC) has claimed that its customer delivery satisfaction is comparable to Building Sensing Enterprise (BSE). As a Data Analyst, I have been tasked with evaluating this claim using inferential statistics. Specifically, I will test whether there is a statistically significant difference between the satisfaction scores of TSC and BSE, based on the 25 observations collected from each contractor.

2. Descriptive Statistics

At face value, TSC’s mean satisfaction score (91.0) appears higher than BSE’s (87.6). However, inferential analysis is required to determine if this difference is statistically significant.

3. Assumption Checks

a) Normality

The Shapiro-Wilk test was applied to both datasets:

• TSC: W = 0.958, p = 0.373
• BSE: W = 0.970, p = 0.653

Since both p-values > 0.05, the null hypothesis of normality is not rejected. Thus, both datasets can be treated as normally distributed.

b) Homogeneity of Variances

• Levene’s Test was performed:
• Levene’s statistic = 0.137, p = 0.713

As p > 0.05, equal variances can be assumed.

Assumption Outcome: Both assumptions of normality and equal variances are met, making the independent samples t-test an appropriate method of analysis.

4. Inferential Analysis

An independent samples t-test (two-tailed) was conducted:

• t(48) = 1.815, p = 0.076

Since p = 0.076 > 0.05, the result is not statistically significant at the 5% level.

5. Interpretation of Results

Although TSC’s mean score (91.0) is slightly higher than BSE’s (87.6), the difference cannot be considered statistically significant. This suggests that the observed difference may be due to random sampling variation rather than a true performance difference.

6. Conclusion

• Assumptions: Normality and equal variance assumptions were satisfied.
• Statistical Test: Independent samples t-test.
• Result: No significant difference (p = 0.076).

Conclusion:

TSC’s claim that its customer satisfaction performance is comparable to BSE’s is supported by the analysis. While TSC’s mean score is marginally higher, the difference is not statistically significant at the 5% threshold. Therefore, IST management can reasonably conclude that delivery satisfaction between the two contractors is statistically similar.

Would you like me to also prepare a visual graph (boxplot + mean comparison) of TSC vs BSE satisfaction scores for your report appendix? This can make your analysis more reader-friendly.