1)Suppose you take a Covid test and it comes back positive, but in reality, you do not have Covid. What is the null hypothesis under consideration? What is the alternative hypothesis? Is this a type 1 or a type 2 error?

2)Suppose we have a

sample average X=0.75 X=0.75

with standard error X=0.33 X=0.33.

What is the 95% confidence interval for XX (assuming we have a large nn)? Would you reject the null hypothesis that H0:=0

H0:=0 for an alternative Ha:>0 Ha:>0?

3)Suppose that you think that is has been raining less in Eugene over the last five years compared to historical averages. So you go find that the average annual rainfall between 2017 and 2021 is 39.339.3 inches with a standard deviation of 4.754.75, while the average annual rainfall between 2006 and 2016 was 4040 inches. Is there statistical evidence of a decrease in rainfall comparing 2017-2021 to 2006-2016?