This is problem number 73 from section 9.3. Uh, this problems talking about healthy bones and that they're the RD a recommended daily allowance of women there recommended you that women between ages of 18 and 24 get 1200 milligrams of calcium. Uh, however, they believe that this intake is actually less, uh, what really happens. So they did a study. They took a random sample of 36 women. And they put all that dad in the mini tab and you have the outputs there actually ran the test, um, for you in the second box. And then they ask us three questions So question letter a. Determine whether there's any out, Lars, and this is sort of a review from way earlier in this book. So if you remember, you have an outlier rule. The outlier rule is 1.5 times the Iike you are like you are that is Q three minus. Q. Once arrange Q three minus Q. One. So we're going to go 1090 0.5 minus 632 0.3, and I will get an I q. R of 458 0.2. Then find out my, uh, 1.5 times i q r rule. We're going to go 458.2. We're gonna take the Ike you are. We're gonna multiply that by 1.5 and I get 687.3 now, to find out if there's any out liars, we're gonna take that value. And we are going to subtract from Q one to get a low point. So anything below that mark is an outlier, and then we're gonna take the 687.3. We're going to add it to Q three and say, Hey, any value above that one is going to be an outlier. So let's start off here with q one is 632.3. We're gonna subtract out at 1.5 rule, so 687 0.3 and we end up with negative 55. Now they tell me my minimum value is 374. So there's no lo outlier, no lo outlier. And then we're going to do the same thing for the high end. We're gonna take you three and we're gonna add in that 1.5 rule and this is going to give me 1777.8. My maximum value here is 1425. You seat in a box there, so there's no hi out liars. There's no outliers here. So now moving on the part beat Interpret the P value in context. Now they tell me in that middle box at second box at the P value all the way. At the end, there is 0.0 It's approximately zero. So to interpret that what a P value means is, if the no hypothesis was true, if the no hypothesis is true, the probability of getting the sample result that we got is the P value. So here we go. If the true calcium intake for 18 to 24 year old women is 1200 milligram. So if that's true and we take a sample size 36 the probability of getting the result we got of 865.2 milligrams is approximately. The P value is approximately zero. So you could see my Senate, Sir. It's a true calcium intake of 18 and 25 year old women is 1200 milligrams. The probability of taking a sample size 36 from the population to get a sample result of 865.2 milligrams is approximately zero. This is one of the sentences that I have my students memorize, which is some blanks in here so they can fill stuff in, And then part see, do these daddy give convincing evidence to support the researchers? Sufficient suspicion carry out attacks. So we're gonna do a state plan. Do conclude here. So I'm going to do this a little quicker here. We've already done a couple of these. So state will perform a one sample T test again. Name of the test, given my awful value to see if there is convincing evidence of support that women have a lower calcium intake than the recommended daily allowance. So I'm sort of writing that Exactly how the questions asked I need to define my mu mu equals a true mean daily intake of calcium for women 18 to 24 year old Uh, my no hypothesis. And I forgot something on here. I need to put, um you in here? Mu equals 1200 milligrams. My alternate hypothesis Mu is less than 1200 milligrams. Okay, so our d a wants us have 1200. We believe there's less than 12 hundreds. That's my ace. Abo and H today plan three things random 36 women were randomly selected, 10% Rule 36 women is definitely less than 10% of all young women and large counts. Thank goodness we took a sample bigger and 30. So I can use the central limit theorem here and say that we can perform a T distribution. The do part and all these values are ah in those charts there. So we know that X bar, my mean, is 856.2 milligrams. I know My standard deviation is 306.7. My t stat value is massive negative 6.73 were over six standard deviations away, which gives me a P value of approximately zero conclusion again. Since the P value is approximately zero, which is less than 00.5 which equals Alfa, we reject the no hypothesis. There is convincing evidence towards the alternate. There is convincing evidence that 18 to 24 year old women consume less than 1200 milligrams of calcium per day