Practice Problem 2 - One Way ANOVA (4 points) Calcium is an...

Practice Problem 2 - One Way ANOVA (4 points) Calcium is an essential mineral that regulates the heart and is important for blood clotting and for building healthy bones. The National Osteoporosis Foundation recommends a daily calcium intake of 1000 to 1200 mg/day. A study was performed to see if there is a difference in mean daily calcium intake in adults with normal bone density, osteopenia, and osteoporosis. The table shows the mean daily calcium intake of each individual from each group. Is there a statistically significant difference between these groups? Normal bone Osteopenia Osteoporosis density 1200 1000 890 1000 1100 650 980 700 1100 900 800 900 750 500 400 800 700 350 800 550 550 700 600 650

Transcript

00:01 Hello, so today i'm going to answer your question about the difference in calcium levels for normal people and individuals that have a specific condition.

00:11 For doing so, i'm going to use a t distribution.

00:13 Why? because your sample size is more than 30, so you can use a normal distribution, but you have to use a t.

00:19 So these are the components that you first need to estimate to use this formula.

00:24 So first we are going to calculate the means.

00:26 So i'm going to calculate the mean for the normal bone against the one that is abnormal or people that have all.

00:32 Osteopenia and osteoporosis.

00:35 For doing so, i use this formula, that is the amount, the addition of all the elements.

00:43 I'm going to write it here because 10 is crossed down.

00:50 I don't know why.

00:51 This is the original formula, and this is the formula you need to use.

00:54 So add each other there, for example, in the case of normal 1 ,200, 1000, and so on, and divided by the sample size in your case 6.

01:01 This is the total, and this will be the meaning for the people that have normal bond density.

01:05 Then i repeat the same process for people that have osteopenia and osteoporosis, then divided by 12.

01:11 This is the value.

01:13 The next step that i need to do is try to find the standard deviation.

01:19 The standard deviation follow this formula, where you need to do each element, subtract the mean, divide by the sample size, and take the square root.

01:26 So that's what i did here.

01:28 So for example, for the first observation, i take the mean that we previously calculated, raised it to the square, and added to the next term, and so on.

01:34 The same for the abnormal bond distribution.

01:38 I obtain the standard deviations.

01:41 Then i just need to replace, so as you may recall the formula, you have the mean one here and the mean two here...

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