Answer:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
The value of r is always between 
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.
Step-by-step explanation:
For this case we know that the correlation between the height and weight of children aged 6 to 9 is found to be about r = 0.8. And we know that we use the height x of a child to predict the weight y of the child
We need to rememeber that the correlation is a measure of dispersion of the data and is given by this formula:
The value of r is always between
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.
Each tablet is 250 milligrams. Your doctor wants you to take 3 grams (g) per day
We know ,
1 gram = 1000 milligrams
250 milligrams makes 1 tablet
so 1000 milligrams makes how many tablets
= 4 tablets
1000 milligrams makes 4 tablets. That is 1 gram = 4 tablets
1 gram = 4 tablets
3 grams = 3 * 4 = 12 tablets
So you need to take 12 tablets per day.
X=36
Divide the corresponding side (16) by 4/7
Answer: green shirts = 6
Blue shirts = 11
Yellow shirts = 4
Red shirts = 7
Step-by-step explanation:
Red shirts = 7
Let green shirts be x.
There are 5 more blue shirts than green shirts. This means:
Blue shirts = x + 5
There are 2 fewer yellow shirts than green shirts. This means:
Yellow shirts = x - 2
There are 28 shirts in total
Red + blue + yellow + green = 28
7 + (x + 5) + (x - 2) + x = 28
7 + x + 5 + x - 2 + x = 28
10 + 3x = 28
3x = 28 - 10
3x = 18
x = 18/3
x = 6
There are 6 green shirts
Blue shirts = x + 5 = 6 + 5 = 11
Yellow shirts = x - 2 = 6 - 2 = 4
Red shirts = 7
Answer:
We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%
Step-by-step explanation:
-From the given information, 
.
-We calculate the confidence interval using this value at 95% confidence level:
![CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585]](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20z%20%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D%5C%5C%5C%5C%5C%5C%3D0.65%5Cpm%201.96%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.65%5Ctimes%200.35%7D%7B12000%7D%7D%5C%5C%5C%5C%5C%5C%3D0.65%5Cpm%200.0085%5C%5C%5C%5C%5C%5C%3D%5B0.6415%2C0.6585%5D)
So, the 95% confidence interval is (0.6515,0.6585).
Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.
