Example: Home wind turbines b We observe: n =12, X, = 14.3 5,. = 4.7 p0 = 10 Ho: \"(IO \"1: #>|O 14.3Io bWegetT= =31? 4.7 ' From table: (12% = 1.80 so we the example of the home wind turbines. So, in that example, we had 12 observations. And we were trjn'ng to test if the expectation of these observations was less than 10 or larger than 10. We collected some data, and here the data we collected gave us an average wind speed of 14.3 over those 12 observations and an estimated standard deviation of 4.7. OK, and let me remind you that the test we're trying to perform is to try to nd evidence that we have enough wind speed to actually proceed to installing and spending money on installing this home wind turbine. 50, clearly, H1 will be that mu has to be larger than 10. That's what we're trying to bring evidence towards. And the status quo is that, in fact, we do not have enough speed. All right, so now I plug in the numbers that I have. So this is square root of n is square root of 12. This is my 25,1; bar. I remove mu 0, right? Here I have to put the number that I actually know, which is mu 0, my edge case. And I divide by Sn, my estimated standard deviation right here. So I just put that in a calculator, and the number that comes out is 3.17. So now, if I want to reject, I need to decide whether this number is larger or smaller than q alpha of a t 11 minus 1 where alpha is, say, 5%, and n we know is 12. All right, so that ends up being q 5% for a t 11 degrees of freedom. So I pull it from a table, and I wl see that this is 1.80. 1.80 is actually smaller than 3.17. So I'm in the rejection region. So what do I do here? I reject. OK, so that's how you build a test. And now I know that this rejection was performed at level alpha, not asymptotic level alpha. Wind turbines Using the data from the wind turbine example, construct a confidence interval at (non-asymptotic) confidence level 95%