James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far less green candies than any of the others and wondered if the true proportion of green candies is lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags of candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he counted, 37 of them were green. James conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of green candies was lower than 12.5%.

(a) H0:p=0.125; Ha:p<0.125, which is a left-tailed test.

(b) Use Excel to test whether the true proportion of green candies is less than 12.5%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

17 1/3

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this