Ian is a phycologist interested in determining the proportion of algae samples from a local rivulet that belonged to a particular phylum. a random sample of 50 alga were obtained and each was categorized as either being cyanobacteria or not. it was found that 38 were, in fact, cyanobacteria. without relying on any previous knowledge ian wanted to estimate the proportion that were cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval. how large a sample size would be required?

16590

Step-by-step explanation:

The formula we use to find the sample size is given by :-

, where p = prior estimate of population proportion.

= Critical z-value (Two- tailed)

E= Margin of error .

Let p be the population proportion of cyanobacteria.

Given : E = 0.01

Critical value for 99% confidence interval :

If Ian does not want to rely on previous knowledge , then we assume p=0.5 because the largest standard error is at p=0.5.

Now, the required sample size =

Required sample size = 16590

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3