Business Context
PulseCart, a grocery delivery app, wants to measure true customer satisfaction with a new subscription plan. Before launching a large customer survey, the research team ran a wording test to check whether a leading question biases responses.
Problem Statement
Two versions of the same satisfaction question were randomly shown to comparable customer samples:
- Neutral wording: "How satisfied are you with the new subscription plan?"
- Leading wording: "How satisfied are you with our convenient new subscription plan?"
A response of 4 or 5 on a 5-point scale is classified as positive. Determine whether the leading wording produces a statistically significant increase in positive responses, which would indicate questionnaire bias.
Given Data
| Question Version | Sample Size | Positive Responses | Positive Rate |
|---|
| Neutral wording | 420 | 214 | 50.95% |
| Leading wording | 400 | 238 | 59.50% |
Use a one-sided test at significance level 0.05, because the concern is specifically whether the leading wording inflates positivity.
Requirements
- State the null and alternative hypotheses.
- Compute the sample proportions for both question versions.
- Calculate the pooled proportion and standard error for a two-proportion z-test.
- Compute the z-statistic and one-sided p-value.
- Construct a 95% confidence interval for the difference in positive response rates.
- Decide whether the leading wording is biased enough to reject as an unbiased questionnaire item.
- Briefly explain one additional design change that would further reduce questionnaire bias.
Assumptions
- Respondents were randomly assigned to one question version.
- Each respondent answered only once.
- Samples are independent.
- Normal approximation is appropriate because both groups have sufficient positive and negative counts.
