To determine the organic material in a dried lake ted, the percent carbon by mass is measured at two different locations. In order to compare the means of the two different locations, it must first be determined whether the standard deviations of the two locations are different. Location1(%C) Location2(%C)
1 10.40 10.10
2 10.20 10.90
3 10.30 10.20
4 10.40 10.70
5 10.20 10.40
a-1. Far each location, calculate the standard deviation and report it.
- location 1:
- location 2:
a-2. What is the calculated F value for comparing the standard deviation?
b. Are the two standard deviations for the locations significantly different at the 95% confidence level?
A. yes.
B. No.
c. What is the calculated t value used to compare the means of these two locations?
d. Are the means for the two different locations significantly different at the 95% confidence level?
A. yes.
B. No.

a-1.- location 1: =0.01- location 2: =0.113

a-2. F= 0.08849

b.  A. yes.

c.  t= -1.020

d. B. No.

Step-by-step explanation:

Location1(%C)             Location2(%C)

      x                  x²                      y                     y²

1   10.40           108.16                  10.10          102.01

2  10.20           104.04                  10.90         118.81

3  10.30           106.09                 10.20          104.04

4  10.40            108.16                  10.70         114.49

5  10.20            104.04                  10.40       108.16        

∑   51.5              530.49                  52.3         547.51      

x`= ∑x/n1 = 51.5/5= 10.3;    y`= ∑y/n2= 52.3/5= 10.46

Sx² = 1/n1-1[ ∑x² - (∑x)²/n1] = 1/4[  530.49 - (51.5)²/5]

        = 1/4[ 530.49 - 530.45] = 0.01

Sy² = 1/n2-1[ ∑y² - (∑y)²/n2] = 1/4[  547.51 - (52.3)²/5]

        = 1/4[ 547.51 - 547.058] = 0.113

F= Sx²/Sy²= 0.01/0.113= 0.08849

The critical region is F ≥ F(0.025) (5,5)= 7.15

and  F ≤ 1/F(0.025) (5,5) = 1/7.15= 0.13986

Since the calculated value of F =0.08849 falls in the critical region we conclude that  the two standard deviations for the locations significantly different at the 95% confidence level.

c.   t= x1`-x2`/ sqrt ( s₁²/n₁ + s₂²/n₂)

t= 10.3-10.46/ sqrt( 0.01/5 +0.113/5)

t=- 0.16/0.15684

t= -1.020

d.  The calculated value t= -1.020   does not fall in the the critical region

t (0.025) (4) = ±2.776  we conclude that the  means for the two different locations are not significantly different at the 95% confidence level.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is