APFIVE In an experiment, a company claims that 75% of its employees are satisfied and a sample of 125 employees yields 87 satisfied employees ($$\hat{p}\approx0.696$$), resulting in a z-test with a p-value of about 0.0816. What would happen if the observed number of satisfied employees increased to 93 (making $$\hat{p}\approx0.744$$)?
| Observed Count | $$\hat{p}$$ | z-score |
|---|---|---|
| 87 | 0.696 | -1.39 |
| 93 | 0.744 | -0.16 |
This table compares the z-scores for different observed counts in a hypothesis test for a population proportion.
The evidence against the company’s claim would be weaker because the computed z-value would be closer to 0, leading to a larger p-value and a failure to reject the null hypothesis.
The test statistic would remain unchanged because the sample size is fixed at 125.
The evidence against the claim would strengthen since an increase in satisfied employees always increases the z-value.
The test would automatically become two-tailed, changing the p-value interpretation.
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