Effect of Sample Proportions on a Z-Test
A study compared the proportion of First Nations children in welfare care (162 out of 1,500) with the proportion of non-Aboriginal children in care (23 out of 1,600). A two-proportion z-test yielded a z-statistic of 11.0 with a p-value near zero. If the number of non-Aboriginal children in care increased such that the two sample proportions became more similar, which of the following would be the most likely outcome?
The test would automatically adjust to a two-tailed test, altering the rejection region.
The z-value would decrease, leading to a larger p-value and weaker evidence against the null hypothesis.
The z-value would remain unchanged because the First Nations data is constant.
The increase in cases would enhance the contrast and further increase the z-value.
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