Alternative hypothesis

$H_a$ (H-a) is a claim about the same population parameter that $H_0$ names, written with $<$, $>$, or $\neq$ instead of an equals sign, so it covers a range of values rather than one. Its job is to say which departures from the null count as evidence, and it is chosen from the question being investigated before any data are seen.

That choice moves the cutoffs, not just the wording. With $H_0: \mu = 100$, $\sigma$ (sigma) known to be 15, $n = 25$ and $\alpha = 0.05$, the standard error is 3. Under $H_a: \mu > 100$ the whole 5 percent sits in the upper tail and the test rejects once $\bar{x}$ (x-bar) passes 104.93. Under $H_a: \mu \neq 100$ that 5 percent splits into 2.5 percent per tail and the cutoffs move out to 94.12 and 105.88. A sample mean of 105.2 rejects under the first and does not under the second, on identical data.

The misuse to name: "the data came out high, so I will use $H_a: \mu > 100$." Picking the direction after seeing which way the sample fell means you would have picked the other direction had it fallen the other way, so the test really rejects whenever $|z| > 1.645$. That has probability 0.10 under a true null, exactly double the 0.05 you claimed.

Write $H_a$ about the parameter, never the statistic: $H_a: \bar{x} > 100$ is not a hypothesis, since $\bar{x}$ is a number already sitting in front of you. And a one-sided alternative gives up the other direction completely. The test above has power 0.0005 against a true mean of 95, which is blind for practical purposes.

Setting up the pair of hypotheses is AP Statistics topic 3.5, Setting Up a Test for a Population Proportion, and topic 4.4, Setting Up a Test for a Population Mean or Population Mean Difference.