I am currently reading the Hypothesis Testing lecture and I found two lines seemingly contradictory. Excerpt below. I have used bold font to highlight the lines in question
The Null and Alternative Hypothesis
The first thing we need to introduce is the null hypothesis, commonly written as H0 . The null hypothesis is the default case, generally reflecting the current common conception of the world. The alternative hypothesis is the one you are testing.
First we state the hypothesis that we wish to test. We do this by identifying a null hypothesis and an alternative hypothesis. The null hypothesis, H0 , is the one that we want to test, while the alternative hypothesis, HA , is the hypothesis that is accepted in the case where H0 is rejected.
I wanted to add one more excerpt of something that appears contradictory
For example, we might estimate a sample mean as 100 , with a confidence interval of 90,110 at a 95% confidence level. This doesn't mean that the true population mean is between 90 and 110 with 95% probability
For example, if our 99% confidence interval for the mean of MSFT returns was (−0.0020,0.0023) , that would mean that there was a 99% chance that the true value of the mean was within that interval.