| BUS105: Statistics |
Q1(b) Inferential Analysis of Customer Satisfaction Scores
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
| Statistic | TSC | BSE |
| Sample Size (n) | 25 | 25 |
| Mean | 91.00 | 87.64 |
| Standard Deviation | 6.34 | 6.76 |
| Minimum | 76.27 | 74.01 |
| Maximum | 100.00 | 100.00 |
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.
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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.