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

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.

Statistics Assignment Answers: Expert Answers on Above Inferential Analysis

Purpose of analysis

The main purpose of the analysis is to test the claim made by TSC that its delivery satisfaction is comparable to BSE. The test will be performed using inferential statistics on two independent samples.

Descriptive statistics

For TSC, the mean value is 91, standard deviation is 6.34 and range is 76.27-100
For BSE< the mean value is 87.64, standard deviation is 6.76 and range is 74.01-100
This indicates that the mean is higher for TSC, but it requires inferential testing.

Assumptions

It is assumed that the normality for both the datasets have p>0.05 and for homogeneity, p = 0.713>.05

Inferential analysis

The performance of independent samples t-test indicates that t(48) = 1.815, p = 0.076.
This indicates that p>0.05 and there is no statistically significant difference in satisfaction scores.

Interpretation of results

TSC’s mean is 91.0 and it is greater than BSE mean 87.6, but there is no significant difference. This leads to the conclusion that the claim of TSC of comparable satisfaction with BSE is supported.

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