Question

Objective: Apply Kruskal's algorithm to find the minimum spanning tree. This activity is designed to encourage collaboration and interaction among classmates and creates engagement that is equitable to face-to-face learning.

Q: A telecommunication company plans to update fiber-optic lines for multiple neighborhoods. It saves the company money if the amount of lines can be minimized. The vertex represents the neighborhood. The distance is marked in units of 10 miles (the weight of each edge is given.) Use the Kruskal's algorithm to find the minimum Spanning tree.

1. Describe Kruskal's algorithm steps in detail. Explain how you used these steps to find the minimum weight for this question. You can label the vertices using letters in your description.

2. What is the minimum weight of the following graph? Show your Spanning tree diagram by attaching a file/image to this discussion. Use the correct units in miles. (1 on graph = 10 miles)
(see the picture attached below)

Note: The cost of the spanning tree is the sum of the weights of all the edges in the tree. There can be many spanning trees; The minimum spanning tree is the spanning tree where the cost is the minimum among all the spanning trees. There could also be many minimum spanning trees.

The minimum spanning tree has direct application in the design of networks. It is used in algorithms approximating the traveling salesman problem, multi-terminal minimum cut problem, and minimum-cost weighted perfect matching.

Answer 1

Explanation:

(1)Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals

express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM

shifts express similar fulfillment. Establish a 90% confidence interval estimate for the difference

and interpret.

p1 – proportion of nurses working day shifts

p2 – proportion of nurses working night shifts

Conditions:

1. Random – assume samples are representative of the populations

2. Independence – it is safe to assume that the samples would be independent of each other

3. 10% Condition – 125 nurses is less than 10% of all nurses working a day shift. 150 nurses is

less than 10% of all nurses working a night shift.

4. Success/Failure -

1 1 2 2 n p n p

ˆ ˆ

    105 10 108 10

1 1 2 2 n q n q

ˆ ˆ

    20 10 42 10

All conditions have been met to use the Normal model for a 2 proportion z-interval.

CI:

1 2

1 1 2 2

1 2

1 2

105 108

ˆ ˆ 0.84 0.72

125 150

ˆ ˆ ˆ ˆ

( ) * ˆ ˆ

(0.84)(0.16) (0.72)(0.28) (0.84 0.72) 1.645

125 150

p p

p q p q

p p z

n n

   

  

  

CI: (0.0391, 0.2009)

We are 90% confident that the true proportion of nurses working a day shift who express positive

job satisfaction is between 3.9% to 20.1% higher than for nurses working a night shift.