Data on fifth-grade test scores (reading and mathematics) for 420 school districts in California yield = 646.2 and standard deviation = 19.5 a. Construct a 95% confidence interval for the mean test score in the population.
b. When the districts were divided into districts with small classes (< 20 students per teacher) and large classes (≥ 20 students per teacher), the following results were found:
Class Size Average (Y-bar) Standard Deviation (Sy)n
Small 657.4 19.4 238
Large 650.0 17.9 182
Is there statistically significant evidence that the districts with smaller classes have higher average test scores? Explain (set up your hypothesis, and clearly state your decision rule).

(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