Day care centers expose children to a wider variety of germs than the children would be exposed to if they stayed at home more often. This has the obvious downside of more frequent colds and other illnesses, but it also serves to challenge the immune system of children at a critical stage in their development. A study by Gilham et al. (2005) tested whether social activity outside the house in young children affected their probability of later developing the white blood cell disease acute lymphoblastic leukemia (ALL), the most common cancer of children. They compared 1272 children with ALL to 6238 children without ALL. Of the ALL kids, 1020 had significant social activity outside the home (including day care) when younger. Of the kids without ALL, 5343 had significant social activity outside the home. The rest of the children in both groups lacked regular contact with children who were not in their immediate families.

a.) Is this an experimental or observational study?

b.) What are the proportions of children with significant social activity in children with and without acute lymphoblastic leukemia?

c.) What is the odds ratio for acute lymphoblastic leukemia, comparing the groups with and without significant social activity?

d.) What is the 95% confidence interval for this odds ratio?

e.) Does this confidence interval indicate that the amount of social activity is associated with acute lymphoblastic leukemia? If so, did the children with more social activity have a higher or lower occurence of acute lymphoblastic leukemia?

f.) The researchers interpreted their study results in terms of the differing immune system exposure of the children, but gave several alternative explanations for the pattern. Can you think of any possible cofounding variables?

a) This is an Observational Study because in this kind of study investigators observe subjects and measure variables of interest without assigning treatments to the subjects. Here, the Gilham et al. (2005) studied two different groups where no treatment or intervention was done. These groups were independent of each other.

b) proportions of children with significant social activity in children with acute lymphoblastic leukemia = 1020/1272 = 0.80

proportions of children with significant social activity in children without acute lymphoblastic leukemia = 5343/6238 = 0.86

c) Odds ratio can be calculated using the following formula:

OR= \frac{a/b}{c/d}

where: a - Number in exposed group with positive outcome(here this means number of children with significant social activity associated with acute lymphoblastic leukemia)

b- Number of children without social activity having with acute lymphoblastic leukemia

c- Number of children with social activity having without acute lymphoblastic leukemia

d- Number of children without social activity having without acute lymphoblastic leukemia

OR= \frac{1020/252}{5343/895}

OR= 0.6780

d) The 95% confidence interval of this Odds Ratio is 0.5807 to 0.7917.

e) Since the odds ratio lies in this confidence interval indicate that the amount of social activity is associated with acute lymphoblastic leukemia. The children with more social activity have a higher occurrence of acute lymphoblastic leukemia.

the answer is c. hope this !

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1