Hypotheses for a Population Proportion

You assume the skeptical claim first because a test only knows how to measure evidence against something fixed. The null hypothesis, H0, pins the population proportion p at one exact number. The alternative, Ha, says p is different from that number, in whichever direction the research question points. You collect data and ask how surprising your sample would be if H0 were actually true. If the sample result would be rare under that assumption, you have evidence against H0 and in favor of Ha. You never start by assuming the thing you want to prove, because then any result would seem to confirm it.

Turning words into symbols means finding the claimed number and the direction of suspicion. A claim like 'more than 60% of drivers speed' gives you the value 0.60 and the direction greater than, so H0: p = 0.60 and Ha: p > 0.60. A claim with no direction, like 'the proportion has changed from 0.5,' gives a two-sided alternative, Ha: p not equal to 0.5. The null always uses an equals sign and a fixed parameter value, never the sample proportion p-hat, because p-hat is just a number you calculated, not something you are testing.

This setup feeds directly into the next steps: computing a test statistic that measures how many standard deviations p-hat sits from the hypothesized p, then finding a p-value from that statistic. Whether the alternative is one-sided or two-sided decides how that p-value gets shaded on the sampling distribution, which later connects to the two types of errors a test can make.