Design an experimental study to investigate the relationship between social media use and self-esteem?

What is your hypothesis?  

What is your independent variable? How will you manipulate the IV?

What is your dependent variable? How will you measure your DV?

What type of hypotheses does the experimental method allow you to test that the correlational method does not? (Note: You can disregard ethical limitations here! Just design an experimental study rather than a purely correlational study).

Use This Table to Calculate r_xy

A copy company uses ten photocopy machines—machines 1 to 5 are model A and machines 6 to 10 are model B. To determine which model to purchase in the future, office managers tabulated the average number of errors per day that each machine made last month, resulting in the following data. You are hired for the statistical consulting on the decision. What would be your advice on the future decision on purchasing a new copy machine?  

Conduct a formal significance test and specify the four steps of hypothesis testing, include all formulas.

Find the minimum and maximum values of the function f(x,y)=x^2 -y^2 with the restriction, x^2 +y^4 =16, using Lagrange multipliers.

Consider the vector field F(x,y,z)=〈 4x^(2) , 7(x+y)^2 , −4(x+y+z)^(2) 〉.

Find the divergence and curl of F.

div(F)=∇⋅F= ?

curl(F)=∇×F= ?

B= {1,x,x^2}

B’={1-x^2, x-x^2, 1+2x-x^2}

T(a+bx+cx^2) = 3a+b+c+(2a+4b+2c)x + (-a-b+c)x^2

a) by direct calculation , compute [P]_B’ , p=7-x+2x^2

b) using basis B={1,x,x^2} , compute [T]_B

c_ compute [T]_B’

Consider the following time series data.

Consider the TOYCO model given below:

TOYCO Primal:

max z=3x1+2x2+5x3

s.t.

x1 + 2x2 + x3 ? 430 (Operation 1)

3x1 + 2x3 ? 460 (Operation 2)

x1 + 4x2 ? 420 (Opeartion 3 )

x1, x2, x3 ?0

Optimal tableau is given below:

a) Suppose that TOYCO wants to change the capacities of the three operations as bT = [460, 500, 400](the new right-hand-side vector). Use the post optimality analysis to determine the optimum solution.

b) Suppose that TOYCO adds a fourth operation with the operation times of 4, 1, and 2 minutes for product 1, 2, and 3 respectively. Assume that the capacity of the fourth operation is 548 minutes. Determine the new optimal solution for this case.

c) Suppose the objective function is changed to z = 3x1 + 6x2 + x3. If the solution changes, use the post-optimal analysis to find the new solution.

d) Suppose TOYCO wants to produce toy planes. It requires 3,2,4 minutes respectively on operations 1,2, and 3. Determine the optimal solution when the revenue per unit for toy planes is $10.

Use the Disk/Washer Method to find the volume of the solid of revolution formed by rotating the region about each of the given axes.

14. Region bounded by: y=4 - x^2 and y=0.

(a) the x-axis (c) y= -1

(b)y=4 (d) x=2

AND

17. Region bounded by: y=1/ sqrt((x^2) +1), x= -1, x=1 and the x-axis.

Rotate about:

(a) the x-axis (c) y= -1

(b) y=1

1. Consider the following random variables based on a roll of a fair die,

(1) You get $0.5 multiplied by the outcome of the die
(2) You get $0 if the outcome is below or equal 3 and $1 otherwise
(3) You get $1 if the outcome is below or equal 3 and $0 otherwise
(4) You pay $1.5 if the outcome is below or equal 3 and get $1 multiplied the outcome otherwise

Which random variable(s) has/have the highest variance?

a. Random Variable 1
b. Random Variable 2
c. Random Variable 3
d. Random Variable 4
e. Random Variable 2 and 3

Calculate and interpret a 95% confidence interval 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6