Can you please tell me if this is right?
Suppose that, from the previous elections in a state, in order for a candidate to the governor to be elected, it is necessary for him to win at least 80% of the votes in the northern section of the state. The governor on duty is interested in assessing his chances of returning to the office and plans to conduct a survey of 2,000 registered voters in the northern section of the state. Apply the procedure to test hypotheses and evaluate the governor's chances of being re-elected, with a significance level of 0.05, if the poll revealed that 1,550 of the 2,000 possible voters in the northern part of the state planned to vote for the governor in turn. Is the sample results close enough to expected to conclude that the difference is due to the sampling error?
$$H_0: p\geq0.80$$ $$H_a: p<0.80$$
The critical value: $z=1.645$
$z=-2.80$ falls in the reject region.
So the null hypothesis is rejected in the level of confidence of 0.05.
80% - 77.5% = 2.5% results significative statistically.
In other words, the evidence does not support the claim that the governor on duty returns to his mansion for another four years.
Is this analysis right?