Question1)

There was a lot of talk among football fans about "deflate-gate" last week (hopefully it's not still going on this week) where the New England Patriots grounds crew seem to have decreased the pressure in the team balls by around 2 PSI from the official value of 12 PSI. (These are Gauge pressures, meaning pressure above 1 atm.) A Physics prof from Boston U. suggested that it may not have been a nefarious plot, but simply a consequence of the fact that it's cold outdoors in Boston and they may have filled the balls indoors. See if this makes sense by calculating the change in pressure (assuming the football had constant volume) between 70 degrees F (nominal inside temperature) and 20 degrees F (a relatively balmy winter-time outside temperature in Boston) from the assumed starting point of 12 PSI.

The Fahrenheit to Celsius conversion is ºC = (ºF – 32)/1.8, there are 14.7 PSI in 1.0 atm, and the volume of a football is 4237 cm³– though you may not even need that last one.

Question 2)

. Imagine you were in the mountains and were desperate for a cup of coffee (or tea, if that's your thing) and the only source of heat you have is a butane cigarette lighter. Could you heat a cup of water at 25 ºC to near boiling with the full capacity of the lighter?

You'll have to make some assumptions about the amount of butane in the lighter and water in your cup, which you should identify; but FYI the density of liquid butane is about 0.6 g/mL, the MW is 58.12 g/mol, and the heat of combustion is -2623 kJ/mol (and of course, the density of water is 1.0 g/mL and the heat capacity is 4.18 J/ºC-g).

Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through e below.

a.) Find the sampling distribution of s^2. Type the answers in ascending order for s^2

(type as integers or decimals)

b. Find the population variance:

c.) Find the sampling distribution of the sample standard deviation.

Daryl is a 32?year?old man who presents with a 6?month history of shortness of breath even during activities that require only minor exertion. He has noticed increasing limitation in his exercise capacity and denies wheezing, cough, or phlegm production. He has smoked for 15 years and continues to smoke. Daryl's father has been told he has early compensated cirrhosis but has never drank alcohol; his mother is in good health. Daryl’s serum protein electrophoretic results are shown below:     Adult reference Values        Patient Results Albumin 3.5?5.0   3.6 ?1 ? Globulins 0.1?0.4   0.0 ?2 ? Globulins 0.6?1.0   0.7 ? ? Globulins 0.7?1.1   0.8 ? – Globulins 0.8?1.6   1.0 Total Protein 6.0?8.0   6.1 Patient’s Electrophoretic Pattern                                    18US MLSC 4051: Clinical Chemistry 4 1. What protein fraction(s) is/are abnormal in the patient’s serum? (0.5 pt) 2. An abnormality in this/these fraction(s) is/are most often associated with changes in what protein? (1 pt) 3.   What is the function of this protein? (1 pt) 4.   Could this protein abnormality be related to both the patient’s symptoms and his father’s cirrhosis? Explain your answer. (1 pt) 5. What other test(s) may be done to confirm this abnormality? (1 pt) 6.   What charge is on the plasma proteins when they are dissolved in the typical pH 8.6 electrophoretic buffer? Explain (1 pt)    7.   Are there conditions that will cause an increase in this protein in the serum? If so, state at least one such condition and list at least three other specific proteins that would be abnormal in addition to this protein. (2.5 pts) 8.   Calculate the Total Globulin levels and the A/G ratio for this patient (1 pt)

For this assignment, you are going to build upon several skills that you've learned:

• Create an object that contains objects.
• Using querySelectorAll to read a nodeList from the DOM.
• Looping through the nodeList then updating the HTML page.

Set up

Create the assignment in a "week6" folder with the typical files:

• index.html
• css/styles.css
• js/scripts.js

This is the standard structure that we'll use in all assignments.

Here is the HTML to use for this assignment. Change the meta author tag to include your name!

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="utf-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">

    <title>Working with Objects and NodeLists</title>
    <meta name="description" content="We want to update an HTML page with information from a data object.">
    <meta name="author" content="C SCI 212 Student">

    <!-- link to external CSS file -->
    <link rel="stylesheet" href="css/styles.css?v=1.0">
</head>
<body>
    <!-- Content of the page goes here. -->
    <h1>Introduction</h1>
    <section class="intro">
        <h2>Introduction</h2>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
    </section>

    <section class="student-info">
        <h2>Student Information</h2>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
        <p></p>
    </section>
    
    
    <!-- link to external JS file -->
    <script src="js/scripts.js"></script>
</body>
</html>

The Problem

We have a JavaScript object that contains student information.

We want to update the HTML page with information from the JavaScript object.

Instructions

1. Use window.onload to set up your program to run after the page has been loaded.
2. Create a JavaScript object that contains the 5 JavaScript objects

Design and construct a computer program in one of the approved languages (C, C++, C#, Java, Pascal, Python, etc.) that will illustrate the use of a fourth-order explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients of a fourth-order Runge-Kutta method. See the Mathematica notebook on solving the equations for 4th order RK method. .DO NOT USE a[1] or a[2] = 1/2. Then, you will use these coefficients in a computer program to solve the ordinary differential equation below. Be sure to follow the documentation and programming style policies of the Computer Science Department. The initial value problem to be solved is the following: x'(t) = 2 x2 cos(4 t) subject to the initial condition: x(0) = 1.0 Obtain a numerical solution to this problem over the range from t=0.0 to t=2.0 for seven different values of the stepsize, h=0.1, 0.05 , 0.025 , 0.0125 , 0.00625 , 0.003125 , and 0.0015625 .

The answer at the end of the integration is about 1.978940602164785990777661.

Hint: It is often helpful to test your program on simple differential equations (such as x' = 1 or x'=t or x'=x) as a part of the debugging process.
Once you have worked these simple cases, then try working the nonlinear differential equation given above for the assignment (with a small stepsize).
Also, check your coefficients to make sure that they satisfy the equations of condition and that you have assigned these correct values to the
variables or constants in your program properly. For example, a common error is to write something like:   a2 = 1/2;   when you meant to write
   a2 = 1.0/2.0;   so please be careful.  

Write down (in your output file or in a text file) any conclusions that you can make from these experiments (e.g., what happens as h is decreased?).

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b)Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0  

   H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We cannot conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.    

Do not reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We conclude that the relationship is significant.

(c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = β₀ + β₁x + ε where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b₀ + b₁x + b₂x²

(a) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x².  (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b) Use α = 0.01 to test for a significant relationship. State the null and alternative hypotheses.

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0   

  H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.   

Do not reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We cannot conclude that the relationship is significant.

(c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b)

Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0 H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0      H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero. H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We cannot conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.    

Reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We conclude that the relationship is significant.

(c)

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A statistical program is recommended.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)ŷ =

(b)

Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.    H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We conclude that the relationship is significant.Do not reject H₀. We cannot conclude that the relationship is significant.    Reject H₀. We cannot conclude that the relationship is significant.Do not reject H₀. We conclude that the relationship is significant.

(c)

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

Consider the following data for two variables, x and y.

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

ŷ =____

(b)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

ŷ =____

(c)Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.)____

**A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =_____

Find the value of the test statistic. (Round your answer to two decimal places.)_____

Find the p-value. (Round your answer to three decimal places.)

p-value = ______

(c)Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

______vehicles per hour