Step 1 :Define the sample sizes and the number of successes for each town: \(n1 = 150\), \(n2 = 200\), \(x1 = 67.5\), \(x2 = 134.0\).
Step 2 :Calculate the pooled proportion: \(pooled\_p = 0.5757142857142857\).
Step 3 :Calculate the standard error: \(se = 0.0533833842528339\).
Step 4 :Calculate the z-score: \(z = -4.121132503665149\).
Step 5 :Calculate the p-value: \(p\_value = 3.7701449761229355e-05\).
Step 6 :Since the p-value is much less than the significance level of 0.02, we reject the null hypothesis. This means that we have strong evidence to suggest that the proportion of people who planned to vote for the proposition is not the same in both towns.
Step 7 :Final Answer: \(\boxed{\text{Reject the null hypothesis.}}\)