Overwhelming statistics

We are in the middle of an election campaign in Australia. The auditor releases a report highly critical of the current government. The TV channel asks viewers to indicate (via the remote control) whether the report would change one's voting intention.

The results? 70% No, 30% Yes. The news presenter says that the results overwhelmingly suggest that the report has little effect on voting intention.

But by looking at the results from another angle, it can also be argued that they overwhelmingly suggest that the report would have major political consequences.

The opposition party is leading the current government by a few percentage points, according to election polls. For simplicity's sake, let's say in Australia, half of the voters are going to vote for the opposition, while the other half want the current government to be returned.

Since the report is highly critical of the current government, we can safely assume that no voters for the opposition party are going to change their intention because of it. So, 100% of this half of the voting population would answer No to the question.

Since the overall results are 70% No and 30% Yes, the other 20% No and all 30% Yes would have come from the other half of the voting population. That means, a majority (60%) of the voters who intend to vote for the government are going to change their mind, just because of an audit report! Overwhelming statistics indeed!

Have fun with statistics.