As a first step in developing a new drug to treat cancer in humans, an initial study of the drug is undertaken in rats. Three hundred rats with cancer are studied, and each is assigned to one of three treatments. One hundred rats are randomly assigned to a high dose of the new drug, 100 are randomly assigned to a low dose, and 100 are randomly assigned to a control group (no drug). After six months, each rat is examined and classified as having developed no tumors, one tumor, or two or more tumors. Which of the following would be an appropriate alternative hypothesis in this study for a chi-square test for homogeneity of tumor response across treatments?A. Ha :Ha : There is no difference in the distribution of tumor status across the three treatments. B. Ha :Ha : There is a difference in the distribution of tumor status across the three treatments. C. Ha :Ha : There is no association between tumor status and treatment. D. Ha :Ha : There is an association between tumor status and treatment. E. Ha :Ha : The proportion of rats with no tumors is the same for each treatment group.

Solution :

Here, we are interested to study if the treatments have any effect on going tumor or not. Actually, this is model is an ANOVA one way layout with a treatment 'drug'.

In this kind of model or ANOVA model, we take the negative statement as our null hypothesis i.e.,

There is no difference in the distribution of tumors states across the three  statements.

Therefore, alternative hypothesis would be :

There is a difference in the distribution of tumor states across the three treatments.

So the correct option is (B).

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)