The following is a solution to number 10 and we're going to see if the days and I think it's january and Maui, there's a town in Maui or city in Maui and we're seeing if it follows a normal distribution, the average daily temperatures In January and there are 20 years worth. So it's like 600 20 or something days. They they looked at and there are two parts to this. The first part Um says, Okay, explain what these percentages mean, and essentially it just means that it's the empirical rule. Okay, so the, the reason why they did 34% and 34% is that makes up 68% and empirical rule says that 68% of the data lie within one standard deviation of the mean. So I'm kind of like looking at the middle of that chart right now and um that's where we get the minus sigma plus sigma. So we have a mean, or this is the at least the hypothesis, the mean was 68. I'm saying that in a race ago and so 68 and the standard deviations for that means 68% of the data is between 64 and 72°.. All right, if you do 68 minus 4, 64 68 plus 4, 72 then 95% lies within two standard deviations in the means. That's where we get the 13.5 and 13.5. If you add 13.5 plus 34 plus 34 plus 13.5, that equals 95%. So two standard deviations, if you take 68 minus two times four, that gives you 60 and then 68 plus two times four, that's 76. So 95% of the data is but then is between 60 and 76 degrees. And then finally, likewise, the 2.35 on either end, If you add all that together, you get basically 100%. So 99.7%, you know anything outside of that is definitely an outlier. So that means in this case Um essentially all the data will be between 56° and 80°.. Okay, so that's the first part, that's kind of the meaning behind that. Now let's look at the actual data. So we have observed days, so 14 data values were 14 days were, you know, within three standard deviations on the low side And then 86 within two standard deviations on the low side, and then 207 within one standard deviation and so on, and so forth. And then to 15, so that's all given to you. And then the expected, I just like we've been doing I did the 2.35 took the percent times the sample size, and that gives me the expected data values. Okay, So now let's take a look at The questions that says, what's the significance level? Well, that's given to you, it's the 1% significance level, and that's gonna be your office, your alphas .1. And then we need to write down our hypothesis. So the null hypothesis is that these are matching, these two distributions are matching. So, in other words, the average daily temp the average daily temperature in january for whatever this town is, I think something somewhere in mali follows a normal distribution with I mean 68° and then standard deviation for all right. And then the alternative is just essentially saying not so, you can pretty that up if you want, but the average daily temperature in january does not follow a normal distribution. Alright. Part B says, what's the test statistic? What's the chi square value? We're gonna use technology to find that. But the second part of that says um have the conditions of inference been met and we look to see to make sure that the expected value is greater are are all greater than five and they are. So if you look at these expected values, they're all greater than five, that's good. And then the last part of this, what type of distribution we're gonna use? We're gonna use the chi square distribution obviously because the chi square goodness of fit test, But we need to say how many degrees of freedom and we're gonna use 5° of freedom since there are 6 um observed values. So there are six different buckets I guess you could think of And -1 is five. Okay, so now let's look at some technology so I'm gonna use the IT4 but you can certainly use different form of software. You can certainly you can even use the the formula if you want. Although that might take a while. So I took the liberty to go ahead and type all this stuff in. If you had a cal can edit or Staten edit At L1 is where my observed values are and then L2, these are my expected values and it should be a mirror image. These data values should be the same once you reach the peak. Okay? So then you go to stat once you type those in and then tests and it's one of the last ones. So I went up first since the chi square G O F. That stands for goodness of fit test. L one is your observed L two is you're expected at least. It is in my case. Now, if you have those switched or if you have them in different columns, you'll need to change those. And then the degrees of freedom in this case is five, so then calculate and that gives us everything we need. So that first part, that's the chi square value and that is point 256 and 7.256, which is a super small one. And if you look at if you look at that p value, I mean, that's one of the biggest p values ever seen. So p values 10.998 I pretty much can't get much better than that. That is a very, very big P value and it is definitely greater than alpha, which means we fail to reject. That's two words, by the way, I fail to reject. H Not All right, So, this does follow, you know, almost identical. And you can kind of see that these data values are really close to the same thing. So, um yeah, so, this does follow a normal distribution and concluding it again, you don't need to write it like this, you can deviate from this, but I would say there is not sufficient evidence to suggest that the average daily temperature in january does not follow a normal distribution With means 68 and standard deviation four Kind of a double negative there. So, another way you could say that is um the average daily temperature in January does in fact follow a normal distribution with mean 68 and standard deviation for