Effect of Sample Proportion on Test Statistic
A company claims that 75% of its employees are satisfied. A one-proportion z-test is conducted with the null hypothesis using a random sample of 125 employees. An initial result of 87 satisfied employees () yields a z-statistic of approximately -1.39. If the number of satisfied employees in the sample had been 93 (), the z-statistic would have been approximately -0.16. How does this change in the sample outcome affect the evidence against the company’s claim?
The evidence against the claim would strengthen since an increase in satisfied employees always increases the z-value.
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 would automatically become two-tailed, changing the p-value interpretation.
The test statistic would remain unchanged because the sample size is fixed at 125.
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