Step 1 :Given values are \(n_1 = 421\), \(x_1 = 354\), \(n_2 = 723\), \(x_2 = 551\), and \(\alpha = 0.02\).
Step 2 :Calculate the sample proportions \(p_1 = \frac{x_1}{n_1} = \frac{354}{421} = 0.8408551068883611\) and \(p_2 = \frac{x_2}{n_2} = \frac{551}{723} = 0.7621023513139695\).
Step 3 :Calculate the pooled proportion \(p = \frac{x_1 + x_2}{n_1 + n_2} = \frac{354 + 551}{421 + 723} = 0.791083916083916\).
Step 4 :Calculate the test statistic \(z = \frac{p_1 - p_2}{\sqrt{p(1 - p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} = \frac{0.8408551068883611 - 0.7621023513139695}{\sqrt{0.791083916083916(1 - 0.791083916083916)\left(\frac{1}{421} + \frac{1}{723}\right)}} = 3.1598446203260133\).
Step 5 :Calculate the p-value using the survival function (1 - cumulative distribution function) of the normal distribution. The p-value is approximately 0.0007892664843697467.
Step 6 :Since the p-value is less than the significance level of 0.02, we reject the null hypothesis.
Step 7 :This means that there is sufficient evidence to warrant rejection of the claim that the first population proportion is equal to the second population proportion.
Step 8 :In other words, there is sufficient evidence to support the claim that the first population proportion is greater than the second population proportion.
Step 9 :The final answer is: The test statistic is approximately \(\boxed{3.160}\) and the p-value is approximately \(\boxed{0.0008}\). We reject the null hypothesis, so there is sufficient evidence to support the claim that the first population proportion is greater than the second population proportion.