Business Context
LearnQuest, an online learning platform, wants to understand whether more skilled users search differently inside the product. The search team suspects that higher-skill users issue fewer but more targeted queries.
Problem Statement
You are given a sample of 12 users with a numeric skill score and their average number of searches per session over the last 30 days. Analyze whether user skill level is linearly associated with search behavior.
Given Data
| User | Skill Score x | Avg. Searches per Session y |
|---|
| 1 | 22 | 8.1 |
| 2 | 28 | 7.5 |
| 3 | 35 | 7.2 |
| 4 | 41 | 6.8 |
| 5 | 47 | 6.4 |
| 6 | 53 | 6.1 |
| 7 | 59 | 5.7 |
| 8 | 64 | 5.5 |
| 9 | 71 | 5.1 |
| 10 | 77 | 4.8 |
| 11 | 84 | 4.5 |
| 12 | 90 | 4.2 |
Use a significance level of α=0.05.
Requirements
- Compute the Pearson correlation coefficient between skill score and average searches per session.
- State the null and alternative hypotheses for testing whether the population correlation is zero.
- Calculate the test statistic and p-value.
- Conclude whether the correlation is statistically significant at the 5% level.
- Estimate the simple linear regression line predicting searches per session from skill score.
- Interpret the result in product terms: what does this imply for search UX design?
Assumptions
- Each user is an independent observation.
- Skill score is measured on a continuous scale.
- A linear relationship is a reasonable first approximation.
- No major outliers dominate the result.
