I have not watched the entire video, but there is a problem at the 2:45 mark. The presenter says that Type II error is represented by 1-alpha. First, I assume they meant to say the probability of Type II error. Second, and more importantly, the probability of Type II error is represented by the Greek letter beta, and power = 1 - beta. (The presenter says power = 1 - alpha.)

Regarding Ngozi's original question (about which type of error is more costly), it's impossible to say without knowing the context, and without having some expertise about that context. Traditionally in psychology and related disciplines, the Type I error was seen as more costly, and statistical power was almost ignored. But the 1977 book by Jacob Cohen on power analysis (and work by others) brought about a shift in thinking. Initially, when sample size estimation came to be seen as important, most folks would estimate the sample size needed to give 80% (or less frequently 90%) power to detect an effect of a given size. Nowadays, one may even see sample size estimates to give 95% power. When alpha = .05 (as it typically does), estimating the sample size needed for 95% power treats Type I and Type II errors as equally important.

HTH.

https://www.sciencedirect.com/book/9780121790608/statistical-power-analysis-for-the-behavioral-sciences

High technical tolerance

For technical demands the borders of error and of uncertainty of measurement are defined to be small, if they don't exceed a third of the borders of error and of uncertainty of measurment of the checked medical product ( § 14.3 MPBetreibV, FRG). So the tolerance of errors is practice is rather liberal in relation to the statistical borders of error (0,05; 0,20).

New borders of significance

There is a discussion of sharper demands for borders of significance for medical studies. Senior peer Bruce Weaver underlined the change of perception of the beta error. Near to Your experience, venerated madame Ngozi Adeleye, I would recommend a slight intervention: Fix the action control limit at 0,025 and 0,10 for alpha and for beta errors. That's the task for Your generation. This fixing will result in sharper decision making about the value of "significant" results especially in medical studies. Give birthing to a new quality of studies.

Hammering tolerance of quality control demands the hammer of precision of the normal.

Hi Bruce Bruce Weaver, thanks for the clarification on the power of the test. I actually meant to state is as 1-beta and the probability of a Type II is actually beta. Martin Wedig, setting new borders for significance levels may be a challenge for us the "new generation" as the "old order" may want to maintain the 1%, 5% and 10% levels. Ashkan Latifi, your argument is germane. It's hard to say which is worse. A lot depends on the data, nature of research and circumstances.