Business Context
InsightLoop, a customer analytics company, tracks whether its survey-based satisfaction estimates are accurate enough to support quarterly product decisions. An analyst wants to verify that the latest estimate is statistically reliable before presenting it to leadership.
Problem Statement
A random sample of customers was surveyed, and the analyst observed the share who reported being satisfied. Your task is to assess the accuracy of this analysis using a confidence interval and a hypothesis test against the companys historical benchmark.
Given Data
| Metric | Value |
|---|
| Total customers surveyed | 400 |
| Customers reporting satisfaction | 232 |
| Sample satisfaction rate | 58.0% |
| Historical satisfaction benchmark | 55.0% |
| Significance level | 5.0% |
Requirements
- Compute the sample proportion of satisfied customers.
- Construct a 95% confidence interval for the true satisfaction rate.
- Test whether the current satisfaction rate is different from the historical benchmark of 55% using a two-sided one-sample proportion z-test.
- Report the z-statistic and p-value.
- State whether the result is statistically significant at α=0.05.
- Explain what the interval and test say about the accuracy and decision usefulness of the analysis.
Assumptions
- The 400 customers were randomly sampled.
- Each survey response is independent.
- The normal approximation is appropriate because np and n(1−p) are both comfortably above 10.
- Nonresponse bias and survey wording effects are not modeled here.
