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Secession polling refers to the process of surveying a group of individuals within a region or state to determine their interest or support for the idea of that region or state becoming independent from the larger political body to which it currently belongs. As demonstrated in the exercise, polls were conducted in Quebec and Texas to measure the percentage of the population in favor of secession.

This type of polling is significant because it captures the sentiments and opinions of the populace regarding political autonomy and sovereignty. The results can have real political implications, influencing decisions made by leaders, informing public debate, and potentially leading towards referendums or legislative actions.

A two-tailed test is a statistical test used to determine if there is a difference between two population proportions in either direction (greater than or less than). Unlike a one-tailed test, which only looks for an effect in one specific direction, a two-tailed test considers both possibilities of deviation from the null hypothesis.

In the context of our exercise, a two-tailed test is appropriate because we are interested in finding out whether there is any difference between the proportions of Quebecers and Texans supporting secession, regardless of which proportion is larger. The test compares the observed difference to what would be expected by random chance alone. If the observed difference is sufficiently large, it is deemed statistically significant, leading us to reject the null hypothesis that there's no difference between the population proportions.

The pooled proportion is a combined measure used in statistics to estimate the overall proportion of a certain characteristic within two or more groups. It is calculated by taking the weighted average of the proportions from each group. In our exercise, the number of supporters in both Quebec and Texas is combined, and then divided by the total number of people polled.

This measure is utilized especially in hypothesis testing when comparing two proportions. By pooling data, we gain a common estimate of the characteristic under investigation which allows for a more powerful test of the null hypothesis, which states that there is no difference between the population proportions.

Statistical significance is a term used to describe whether the result of a statistical test is unlikely to have occurred by random chance, given a specified significance level. The level, often set at 0.05 or 5% risk of concluding a difference exists when there is none, sets the threshold for rejecting the null hypothesis. In simpler terms, if a test result is statistically significant, it means there is enough evidence to suggest that the observed effect or difference is real and not due to random fluctuation in the data.

In the secession polling exercise, if the Z-score obtained from the two-tailed test exceeds the critical value at the chosen significance level, we have enough justification to conclude that there is a statistically significant difference between the population proportions of Quebecers and Texans who support secession.