what is Type I and II error

It's among the fundamental of statistics.

First, you have a null hypothesis (H0).
Say, H0 = the mean exam score is 50.
Then the alternative hypothesis (H1) would be
the mean of exam score is NOT 50
(Just treat H1 as the compliment of H0)

Then you assume the null hypothesis is correct.
Suppose it turns out that the sample mean score is statistically different from 50, then you reject the null hypothesis in favour of the alternative hypothesis. But in fact, the population mean is NOT statistically different from 50 (say, 50.3, which is very close to 50), and if you conduct survey of the whole population, you should not reject the null hypotheeis. In this case, just as the sample statistic leads you to rejection of H0 but the popuatlion statistic doesn't, we conclude that you've committed Type 1 error.

Let's say, on the contrary, you assume the alternative hypothesis is correct.
Suppose it turns out that the sample mean score is not statistically different from 50, then you reject the alternative hypothesis in favour of the null hypothesis. But if fact, let's say, the population mean is statistically different from 50 (say, 59, which is quite far from 50), and if you conduct a survey on the whole population, you should not reject the alternative hypothesis. In this case, just as the sample statistic leads you to rejection of H1 but the population statistic doesn't, you've committed Type 2 error.

The benchmark is t-statistic (actual mean - postulated mean) / standard deviation, and if the sample size is large enough (>30), then z-score is a good approximation of the t-statistic by the law of large numbers (L.L.N.).
Normally we use 1%, 5% or 10% significance levels (depending on your subjective choice of sensitivity. The more sensitive to errors, the lower the significance level). And if the t-stat is above a certain threshold corresponding to the significance level (say z > 1.96 for 2-tailed test, 5% s.i.), then H0 is rejected.