As part of the quality-control program for a catalyst manufacturing line, the raw materials (alumina and a binder) are tested for purity. the process requires that the purity of the alumina be greater than 85%. a random sample from a recent shipment of alumina yielded the following results (in percent):
93.2 87.0 92.1 90.1 87.3 93.6
a hypothesis test will be done to determine whethe or not to accept the shipment.

(a) state the appropriate null and alternate hypotheses.
(b) compute the p-value.
(c) should the shipment be accepted? explain.

We accept the alternate hypothesis that the purity of the alumina is greater than 85% and hence, the shipment should be accepted.          

Step-by-step explanation:

We are given the following in the question:  

93.2, 87.0, 92.1, 90.1, 87.3, 93.6

Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 7.0225 +12.6025 + 2.4025 + 0.2025 + 10.5625 + 9.3025 = 42.095

Sample size, n = 6

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

We use One-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

The p-value is 0.003969.

Since, p-value < 0.05

We reject the null hypothesis and fail to accept it.

We accept the alternate hypothesis that the purity of the alumina is greater than 85% and hence, the shipment should be accepted.

i will pick c put check it over to be sure

step-by-step explanation:

-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