Step 1 :Calculate the sample proportions for 2016 and 2018. For 2016, the sample proportion (p1) is \(\frac{533}{533 + 455} = 0.539\). For 2018, the sample proportion (p2) is \(\frac{470}{470 + 515} = 0.477\).
Step 2 :Calculate the pooled proportion (p), which is \(\frac{533 + 470}{533 + 455 + 470 + 515} = 0.508\).
Step 3 :Calculate the test statistic (z) using the formula for the z-score of a proportion: \(z = \frac{p1 - p2}{\sqrt{p * (1 - p) * [(1/n1) + (1/n2)]}}\), where n1 and n2 are the total number of adults surveyed in 2016 and 2018, respectively.
Step 4 :Substitute the values into the formula: \(z = \frac{0.539 - 0.477}{\sqrt{0.508 * (1 - 0.508) * [(1/988) + (1/985)]}}\).
Step 5 :Calculate the above expression to get the test statistic: \(z = \frac{0.062}{0.022} = 2.82\).
Step 6 :\(\boxed{z = 2.82}\) is the final answer.