Project Detail

Description

I need a skilled expert in Statistical Math. I have a project consisting of 5 statistical math problems and 2 quadratic equations. Written work needs to be original. My allowance for this assignment is approx $75.

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Assignment as follows:

Objective 1: Graph basic functions of one variable.

Task:

A.
Given f(x) = –3x + 7
1. Graph f(x).
2. Label the graph.

B.
Given f(x) = –3x2 + x – 5
1. Graph f(x).
2. Label the graph.
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Objective 2: Solve quadratic equations in one unknown both algebraically and graphically.

Task:

A.
Solve the following quadratic equations. Make sure to show all your work. Do not use any method (e.g., factoring, completing the square, quadratic formula, graphing) more than twice. Use the graphing method at least once and clearly identify the solutions.

1. 3x2 + 11x – 20 = 0
2. x2 + 3x - 4 = 0
3. 3x2 – x – 1 = 0


B.
Identify the methods you used to solve each equation in part A.

Note: To demonstrate the graphing method, it is important to demonstrate where the solutions and vertex lie on the graph of the equation.
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Objective 3: Explain randomization, replication, comparison, and control in experiments.

Introduction:

A scientist was hired to determine which brand of toothpaste is more effective in preventing cavities in children. Thirty children volunteered to participate in the experiment from which the scientist randomly created two groups of 15 children. The first group was given Brand A toothpaste, and the second group was given Brand B toothpaste. All of the children were given detailed directions describing when and how they should brush their teeth. After six months the children were taken to the same dentist and the number of cavities each child had was recorded. This data was used to determine which toothpaste is more effective.


Task:

A. In a discussion of variables, do the following:

1. Identify something the scientist tried to control in this experiment.
2. Identify something the scientist did not consider controlling or was unable to control in this experiment.
3. Explain the adverse effects this might have had on the collected data.

B. In a discussion of replication, do the following:

1. Explain how replication was used in this experiment.
2. Explain why it is important.


C. The scientist randomly created the two groups. Instead, the scientist could have divided the two groups based on some common characteristic, such as age or gender. Explain the adverse effects this might have had on this experiment.

D. In a discussion of comparison, do the following:

1. Explain the role that comparison plays in experiments.
2. Explain what was compared in this experiment.

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Objective 4: Explain the Law of Large Numbers.

Task:

Write a brief essay (suggested length of 2 pages) in which you:

A. Define the Law of Large Numbers.

B. Explain the Law of Large Numbers in your own words using a coin toss as an example.

C. Apply the Law of Large Numbers

1. Explain how the following scenario is possible, using a coin toss and fictitious data: As the number of trials increases, the differences between the number of actual and expected successes tends to grow, but the difference between the percentage of actual and expected successes tends to decrease.

Note: See the Attachment for a table that works well to present the information. It is recommended by not required.

2. Answer the following question and explain your answer: Is it true that if I flip a coin 1,000 times I will get heads 500 times?

3. Answer the following question and explain your answer: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?
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Objective 5: Construct simple hypothesis tests for means and proportions.

Introduction:

A potato chip company packages its potato chips into 12.0 ounce bags. You find it hard to believe that the bag contains enough potato chips to weigh 12.0 ounces and would like to make an official complaint. Before doing so, you decide to run an experiment so that you can have some confidence that the company’s claim is incorrect. Over the next several months you buy 30 bags of potato chips and weigh the contents of each one. You discover that the mean weight is 11.9 ounces with a standard deviation of 0.4 ounces. You decide that you will only complain if you can be 95% sure that the bags do not contain at least 12.0 ounces of potato chips. You decide to construct a hypothesis test.

Task:

A. Determine if this is a one-tailed or two-tailed test. Justify your decision.

B. State the null hypothesis and alternative hypothesis, including the parameters on both statements. Your null hypothesis should assume the company’s claim is correct.

C. In a discussion of type I errors, do the following:

1. Define the term type I error.
2. Explain what a type I error is in terms of this problem.

D. In a discussion of level of significance, do the following:

1. Define the term level of significance.
2. Identify the level of significance for this problem.

E. Calculate the test statistic as a z-score by using the z-test formula. Show all relevant work.

F. Using a standard table, you determine that the critical value is –1.645.

1. Determine if the test statistic allows you to reject the null hypothesis.
2. Explain how you reached this conclusion, including a comment relating the results to the original problem.
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Objective 6: Use relevant quantitative problem-solving strategies and techniques to solve multi-step problems.

Introduction:

There are two companies that sell widgets. Both companies sell the widgets to the general public for the same price. In order to earn business, Company A offers a special 25% discount on each order. In response, Company B offers a 35% discount on the portion of the price that exceeds $50. Both discounts are rounded to the nearest cent. If you place an order for $50 or less, it is less expensive to order from Company A. If you place a large enough order, it will be less expensive to order from Company B. At what price does it become less expensive to order from Company B?

Task:

A. You can estimate the answer by considering hypothetical orders and comparing the discounts each company would provide.

1. Create and properly label a table of data demonstrating this technique. The table should include at least four hypothetical orders and should estimate the answer within a $50 range. Each row will represent a hypothetical order. The first row will represent a $50 order and each additional row will represent orders in $50 increments (i.e., $100, $150). The table should include three columns. The first column is the order amount, the second column is the discount that Company A would give, and the third column is the discount Company B would give.

2. Specify the $50 range that the answer could be within.

3. Explain how you used your table to determine the $50 range.


B. Determine algebraically the exact price at which Company B offers you the same discount as Company A. Make sure to show all relevant work.


Note: You will need to develop two algebraic equations—one for company A and one for company B. Start with company A and write down exactly how you obtained your prices for the table in part A. Notice the pattern and replace the numbers that are changing with variables. Test your equation and see if you obtain the correct answer for different order amounts. Use the same variables for company B, and follow the steps you used for company A. The pattern for company B is harder to extract. Now, solve the equations simultaneously by substitution or elimination.


C. In order to find the better price for company B, do the following:

1. Determine the exact price at which it becomes consistently less expensive to order from Company B.

2. Explain how you reached this conclusion.
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Objective 7:
Describe given mathematical procedures clearly and correctly.

Communicate mathematical reasoning in written form.

Communicate mathematical equations in written form.

Communicate the results of a calculation in written form.

Introduction:


By using a ruler, you determine that the distance between two cities on a map is 3.4 inches. According to the map’s scale, 2 inches represents 75 miles. What is the actual distance between the two cities?


Task:

Write an essay (suggested length of 1 page) in which you communicate mathematical information in written form. Include the following:


A. Provide a brief paragraph in which you explain the general procedure used to identify and set up a proportion problem.

Note: You should not refer to the problem in the introduction to this task at this point. Discuss proportions in general terms.


B. Solve the problem in the introduction to this task using a proportion by doing the following:

1. Write a proportion that correctly represents the problem. Remember to include the units in the proportion.

2. Use the proportion you wrote in part B to solve the problem, showing all relevant work.


C. Explain the reasoning behind the proportion you set up (e.g., how did you determine the two ratios in the problem, and how do you know if they are equivalent?).


D. Explain (suggested length of 1–2 paragraphs) each step used to solve the proportion. Your explanation should include the original proportion, the equation at each step, and the final equation with the unknown equal to some number. Remember to include the units in your explanation. (Use complete sentences, not mathematical symbols, to explain the steps.)

E. Briefly explain (suggested length of 1–2 sentences) what the answer means in terms of the original problem.