An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won

An analysis of the results of a football team reveals that whether it will win its
next game or not depends on the results of the previous two games. If it won its
last and last-but-one game, then it will win the next game with probability 0.6; if
it won last-but-one but not last game, it will win the next game with probability
0.8; if it did not win the last-but-one game, but won the last one, it will win the
next game with probability 0.4; if it did not win the last-but-one nor the last game,
it will win the next game with probability 0.2. The dynamics of consecutive pairs
of results for the team follows a discrete time Markov chain with state space S =
{(W, W), (L, W), (W, L), (L, L)}, where W and L means the team won and lost
respectively. To simplify the notation put 1 ≡ (W, W), 2 ≡ (L, W), 3 ≡ (W, L) and
4 ≡ (L, L), so that the state space becomes S = {1, 2, 3, 4}.
i. Write down the transition probability matrix for the chain.
ii. Find the mean number of consecutive games the team won

An experiment was conducted to determine the effect of a high salt mean on the systolic blood pressure (SBP) of subjects. Blood pressure was determined in 12 subjects before and after ingestion of a test meal containing 10.0 gms of salt. The data obtained were:

1. Is a one-sided or two sided test needed here?
2. What is the mean SBP for each time period?
3. What is the standard deviation for each time period?
4. Which statistical test is appropriate to use on these data?
5. Carry out the hypothesis test(s) in question in above d. Use α=0.01
6. Are the means statistically different?
7. Find the 99% confidence interval for the difference of the two means on SBP. Interpret your finding                                                                                     

a rocket rises vertically from rest, with an acceleration of 3.2 m/s(s) until it runs out of fuel at an altitude of 845 m. After this point, its acceleration is that of gravity, downward. what is the velocity when the rocket runs out of fuel? how long does it take to reach that point? what is the maximum altitude and how long to reach it? what is the velocity when it strikes earth? how long is the rocket in the air?

1. A new program is developed to increase the overall number of runs for Major League Baseball teams by an outside sporting company, Run Boys Run. In 2015, the average number of runs scored for the entire season by a sample of 25 teams is 690.24. The population standard deviation is 58.36.

1. Find the standard error.

2. Identify the upper and lower z score for a 95% confidence interval for µ.

3. Calculate the upper and lower bounds of the confidence interval.

For each of the following questions, report 1) the appropriate statistical test or estimation procedure to use, 2) the null and alternate hypotheses, 3) the test statistic, 4) the P value, 5) whether you accept or reject the null, then 6) a sentence or two about what the results mean.

Also answer this subpart: What is the relationship between age and height of children? Display data using one graph.

When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, for computed test statistics, t^₂ = F. To demonstrate this relationship, use the following example. Fourteen randomly selected students enrolled in a history course were divided into two groups, one consisting of 6 students who took the course in the normal lecture format. The other group of 8 students took the course as a distance course format. At the end of the course, each group was examined with a 50-item test. The following is a list of the number correct for each of the two groups.

1. a-1. Complete the ANOVA table. (Round your SS, MS, and F values to 2 decimal places and p value to 4 decimal places.)

1. a-2. Use a α = 0.01 level of significance. (Round your answer to 2 decimal places.)

2. Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. There is any difference in the mean test scores.

Complete the program used on the instructions given in the comments:

C++ lang

#include <string>

#include <vector>

#include <iostream>

#include <fstream>

using namespace std;

vector<float>GetTheVector();

void main()

{

vector<int> V;

V = GetTheVector(); //reads some lost numbers from the file “data.txt" and places it in //the Vector V

Vector<int>W = getAverageOfEveryTwo(V);

int printTheNumberOfValues(W) //This should print the number of divisible values by 7 //but not divisible by 3.

PrintIntoFile(W); //This prints the values of vector W into an output file “output.txt”

}

As you see in the main program, there are four functions. The first function is called “GetVector()” that reads a set of integer, place them into the vector V, and returns the vector to the main program.

The second function is called “GetAverageOfEveryTwoNumber() that takes a vector “V” and finds the average of every two consecutive numbers, place the values into another vector called “W” and returns it to the main program. For example if the Vector is:

10 20 30 40 50 60 70 80 90 100

Then vector “W” should be:

15 25 35 45 55 65 75 85 95

Because (10+20) divided by 2 is 15, and so on.

The next function takes the vector “W” and count how many of the values are divisible by “7” but not divisible by “3”

Finally the last function prints the vector “W” into an output file called “output.txt”

Calculate ANOVAs for the following two problems. Show all your work.

First-born children tend to develop language skills faster than their younger siblings. One possible explanation is that they have undivided attention from their parents. If this is correct, then twins should show slower language development than single children, and triplets should be even slower. The following hypothetical data demonstrate potential measure of language skill from such a study. Do the data indicate significant differences?

Single Child: 8, 7, 10, 6, 9

Twin: 4, 6, 7, 4, 9

Triplet: 4, 4, 7, 2, 3

This study examined how long it took for mothers to get their children back home, when the children were 5 months, 20 months, and 35 months old.

5 months: 15, 10, 25, 15, 20, 18

20 months: 30, 15, 20, 25, 23, 20

35 months: 40, 35, 50, 43, 45, 40

(MUST BE DONE IN C (NOT C++))

Instead of using two different variables, define a structure with two members; one representing the feet and the other one representing the inches. You will also use three functions; one to initialize a structure, another one to check the validity of its values and one last one to print them out.

First, go ahead and define your structure. Next, declare a structure of this type inside main. Then, call your first function (this is a initialization function). This function will be of type structure, it will receive zero parameters and it will return a structure. Inside the function, ask the user for the height of the student. In other words, you will use this function to initialize the structure you have in main.

When done, call a second function (this is checking the function). To this function, you will send your structure. The function will not return anything and it will validate the values inputted by the user. If any of the values is not in the right range (between 5’ 8” and 7’ 7”), display an error message and exit the program. Make sure to also check for negative values.

Lastly, if the program didn’t exit, call the last function (this is printing the function). This function will receive a structure, it will not return anything and it will display the values of the two members of the structure.

Instead of using two different variables, however, we will define a structure with two members; one representing the feet and the other one representing the inches. We will also use three functions; one to initialize a structure, another one to check the validity of its values, and one last one to print them out.
First, go ahead and define your structure. Next, declare a structure of this type inside the main. Then, call your first function (the initialization function). This function will be of type structure, it will receive zero parameters and it will return a structure. Inside the function, ask the user for the height of the student. In other words, you will use this function to initialize the structure you have in the main. When done, call a second function (the checking function). To this function, you will send your structure. The function will not return anything and it will validate the values inputted by the user. If any of the values is not in the right range (between 5’ 8” and 7’ 7”), display an error message and exit the program. Make sure to also check for negative values.
Lastly, if the program didn’t exit, call the last function (the printing function). This function will receive a structure, it will not return anything and it will display the values of the two members of the structure.

Use C code to solve this problem.