In a study investigating screen time and well-being, a researcher explored whether there was a correlation between the number of hours spent on smartphones per day and self-reported life satisfaction ratings.
The researcher randomly selected 19 participants from a local college.
Each participant recorded their daily smartphone screen use (in hours) and rated their overall life satisfaction on a scale of 1 to 10 (where 10 indicates high satisfaction).
The researcher proposed a non-directional (two-tailed) hypothesis, stating that there would be a correlation between daily smartphone hours and life satisfaction ratings.
The researcher chose to use the 5% level of significance and calculated a Spearman's rho correlation coefficient of 0.468.
Table 1 Critical values of Spearman's rho (rsr_srs)
| Level of significance for a one-tailed test | 0.05 | 0.025 |
|---|---|---|
| Level of significance for a two-tailed test | 0.10 | 0.05 |
| N = 17 | 0.414 | 0.485 |
| N = 18 | 0.401 | 0.472 |
| N = 19 | 0.391 | 0.460 |
| N = 20 | 0.380 | 0.447 |
| N = 21 | 0.370 | 0.435 |
Note: The calculated value of rho must be greater than or equal to the critical value to be significant.
Identify the appropriate critical value from Table 1. Explain your choice.
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