1.- The pulse rate of a man due to the effect of Amtas AT 25 mg on different days in a month were found to be.
66, 65, 69, 70, 69, 71, 70, 63, 64 and 68.
Discuss whether the mean pulse rate of the man in the month is 65. Assume significance level is 0.05.

• State Null and Alternative hypotheses (3 points):
• Compute Test Statistic (3 points):
• Compute critical value or pvalue (3 points):
• Decision and conclusion in terms of the problem (4 points):

2.Compute and interpret a 95% confidence interval for the mean pulse rate of subjects from problem 1.

• Compute confidence interval (4 points):
• Interpret confidence interval (4 points):

3.- In an experiment to investigate the possible protective effects of vitamin C against rabies 98 guinea-pigs were given a small dose of fixed rabies virus. Of these, 48 were also given vitamin C, the rest were not. Table 1 gives the number that died or survived under each treatment. Deaths occurred in 35% of the treated and 70% of the control animals. Carry out a test with Yate’s correction to decide if vitamin C is effective against rabies.
Table 1.

• State Null and Alternative hypotheses (3 points):
• Compute Test Statistic (3 points):
• Compute critical value or pvalue (3 points):
• Decision and conclusion in terms of the problem (4 points):

4. The scutum widths of ticks collected from three cotton-tail rabbits were measured and the data are given in Table 2. Using Satterthwaite’s rule to determine the appropriate number of degrees of freedom (unequal variance), carry out t tests to decide which, if any, of the mean scutum widths differ significantly. Make the comparisons with Bonferroni’s correction and without a correction for the number of comparisons.

Table 2. Number of ticks, mean scutum width in microns and standard deviation of the mean width in microns, taken from each of three rabbits

For each comparison state: – State Null and Alternative hypotheses (4 points):

• Compute Test Statistic (5 points):
• Compute critical value or pvalue (with and without correction) (6 points):
• Decision and conclusion in terms of the problem (with and without correction) (6 points):

5.- We want to compare the effect on sleep of two different drugs (hyoscyamine and Hyoscine) on patients. How many patients would you need to use in order to decide if hyoscyamine increases the amount of sleep by at least 30 minutes while keeping the probability of making a Type I error to less than 5% and the probability of making a Type II error to less than 10% (=0.9)? From a pilot sample we have, sd hyoscyamine=1.79 and sd Hyoscine=2.
Write the correct formula to use (3 points):
Write formula with values plugged in (3 points):
Sample size needed per group (3 points):
6.- An experiment was performed in which tick larvae of the species Haemaphysalis leporispalustris were collected from four cotton-tail rabbits.
 
Table 3 Scutum widths, cottontail rabbits in microns, of tick larvae taken from four Rabbits.

Carry out a one way ANOVA test.

• State Null and Alternative hypotheses (3 points):
• Calculate the ANOVA table (4 points):
• Compute pvalue (3 points):
• Decision and conclusion in terms of the problem (4 points):

7.- We consider an experiment of the diet of rats where we examined the extent to which the freshness of the lard and the sex of the rats affected the weight gained by the rats. Table 4 The weight (in grams) gained by male rats fed on fresh lard and on rancid lard , and by female rats fed on fresh lard and on rancid lard.
Table 4.

Carry out a two way ANOVA test.

• Calculate the ANOVA table (5 points):
• Compute pvalues for overall effect, sex effect, diet effect and interaction effect (6 points):
• Decision and conclusion in terms of the problem for each one of the tests (6 points):

8.- Find the correlation coefficient and the equation of the regression line of the following values of x and y.
{(x,y)}={(1,2),(2,5),(3,3),(5,8),(5,7)}

• Correlation coefficient (4 points):
• Regression line (4 points):

You can select any topic from below
Option 1, False Proofs: There are many falseproofs. For example, the following article is an MIT student project:•Xing Yuan, Mathematical Fallacy Proofs http://dspace.mit.edu/bitstream/handle/1721.1/100853/18-304-spring-2006/contents/projects/fallacy_yuan.pdf
You also see two other examples in our lecture, Proof Techniques (1), Introduction. For this project, you need to search the Internet for more new false proofs. Do not use the examples from our lectures and Yuan’s paper. For each false proofyou use, please explain what lead to the false proof, and how the false proof helps students learn and understandand/orenhance your teaching
Option 2, Analysis and Classification of Student mistakesand difficulties: Students often have difficulties and make mistakes in arithmetic,algebra, trigonometry, and calculus. Why? What kind of mistakesand difficulties do theymakeor have? How can you help? You may read the following articles from the following link:https://www.semanticscholar.org/paper/Classifying-students-mistakes-in-Calculus-Hirst/436f1e13390e367c9647d493a5b462561d63b003

• Keith Hirst.Classifying Students’ Mistakes in Calculus
• Nourooz Hashemia,*, Mohd Salleh Abua , Hamidreza Kashefia , Khadijeh Rahimib Undergraduate students’ difficulties in conceptual understanding of derivation.

 If you have taught or tutored before, you may collect the mistakes that your students made, then classify and analyze them. You may also develop a plan how you would apply your findings in your classroom.
Direction to be followed
1.Excluding the title and reference pages, your paper musthave at least 10 pages with double line space. Each missing page will result in a deduction of 15 points in addition to the deductions based on the following rubrics
2.(5 points) Professional appearance and format of your paper: The margins are not more than 1” from each side; the font size should not be larger than 12; and the fontcan be Calibri, or Times New Roman.  The paper must be numbered. The sizes of tables and picturesneed to be reasonable. Your paper should be organized in the following format:a.Project title, names of authors, emails and affiliations (optional)b.Project summary, abstract, and/or objectivesc.Project Body (you may use sections, bullets tables, pictures)d.Acknowledgement (if applicable)e.References:If you obtained any information from the Internet, include the URL.  Youneeduse the MLA (Modern Language Association) citation style, or the Chicago citation style, or the style of a reputable mathematical journal, for example, the Journal of Mathematical Analysis and Applications (http://www.elsevier.com/wps/find/journaldescription.cws_home/622886?generatepdf=true)
3 .(5 points) Summary or abstract of your project. You may include objectivestatements. a.Project title, namesof authors, emails,affiliations, abstract should be included in the title page

4. (15 points) Difficulty and complexity: There are four options for your project (see the next page). For Project Option 1 and 2, the difficulty refersto the level of school mathematics from the lowest, arithmetic,to the highest, calculus II. For Project Option 3, your project needs to be at least at the level you taught, teach, or will teach. The appropriatelength of the project is also a consideration of difficulty, thoughthe minimum length is 10 pages with double space. An unnecessarily lengthy paper will not be considered more difficult. Difficulty may mean complexity. Use and inclusion of definitions, theorems and proofs will reflect difficulty and complexity. The more difficult the mathematics is, the more points you may earn.
5. (15points) Originality or creativity: The first meaning of originality is that your paper must be your own work. Plagiarism is prohibited, and hence will resultin 0 for the entireproject. Anymaterials taken from the Internet, publications and other people’s work must be well cited. The second meaning of originality is that your work has not been seen on the Internet and in publications. Originality may also mean creativity. The more original work your project has, the more points you may earn.
6. (60 points) Readability and Communication: clear and correct calculation, derivation, proofs, applications and explanation; sufficient and appropriate examples; real world examples, particularly related to your students, school and community (this also contributesto originality); smooth connection and transition among concepts, definitions,theorems, examples, and explanations; use of pictures, diagrams, and tables; easiness for understanding; appropriate citation; completeness of the project; fun to read.

7.Correctness: mathematically your project must be correct. Errors and mistakes in mathematics will be subject to deduction of points you earn. Errors and mistakes inother areas (English, Education, Science…) may or may not cause a deduction, depending on the nature and significance of the errors andmistakes.
8.The instructor retains the final interpretation of the grading rubrics

Name: Last ______________________ First_______________________ Section # _________
ID # __________________________________(at least the last 4 digits)
Signature Assignment Math 1315
1. Use Gauss-Jordan Elimination to solve the following system of equations . You must show all of
your work identifying what row operations you are doing in each step. Do not use a graphing
calculator in order to reduce the matrix or you will not receive credit for the problem..
2x – 4y + 6z = – 2
– x + 3y – 3z = 1
– x + 2y + 2z = -4
x = _________
y = _________
z = _________
3. Mike has $235,000 he wishes to invest in two rental properties. One yields 10% and the other
yields 12%. For safety he wants to split his investment between the two properties instead of
investing all of his money in the higher yielding rental property. If his goal is to achieve a total income
earned of $25,000 a year from these two properties, how much money should he invest in each
property. You must show your work illustrating how you calculated your answer in order to get credit
for this problem.
Amount invested in property yielding 10% ________________
. Amount invested in property yielding 12% ________________.
4. A. What would be your monthly mortgage payment if you pay for a $250,000 home by making a
20% down payment and then take out a 3.74% thirty year fixed rate mortgage loan where interest is
compounded monthly to cover the remaining balance. All work must be shown justifying the following
answers.
Mortgage payment = _______________
B. How much total interest would you have to pay over the entire life of the loan.
Total interest paid = __________
C. Suppose you decided to pay for this house by taking out a fifteen year 3.04% fixed rate mortgage
instead of the thirty year 3.74% fixed rate mortgage. What would be your required monthly
mortgage payment for this 15 year mortgage assuming you still make the same 20% down
payment.
D. How much interest would you have saved by taking out the fifteen year fixed rate mortgage
instead of the thirty year fixed rate mortgage.
Interest saved = _______________
E. Taking the above data into account, write a short paragraph comparing what you feel are
the pros and cons of each type of mortgage.

You can select any topic from below
Option 1, False Proofs: There are many falseproofs. For example, the following article is an MIT student project:•Xing Yuan, Mathematical Fallacy Proofs http://dspace.mit.edu/bitstream/handle/1721.1/100853/18-304-spring-2006/contents/projects/fallacy_yuan.pdf
You also see two other examples in our lecture, Proof Techniques (1), Introduction. For this project, you need to search the Internet for more new false proofs. Do not use the examples from our lectures and Yuan’s paper. For each false proofyou use, please explain what lead to the false proof, and how the false proof helps students learn and understandand/orenhance your teaching
Option 2, Analysis and Classification of Student mistakesand difficulties: Students often have difficulties and make mistakes in arithmetic,algebra, trigonometry, and calculus. Why? What kind of mistakesand difficulties do theymakeor have? How can you help? You may read the following articles from the following link:https://www.semanticscholar.org/paper/Classifying-students-mistakes-in-Calculus-Hirst/436f1e13390e367c9647d493a5b462561d63b003

• Keith Hirst.Classifying Students’ Mistakes in Calculus
• Nourooz Hashemia,*, Mohd Salleh Abua , Hamidreza Kashefia , Khadijeh Rahimib Undergraduate students’ difficulties in conceptual understanding of derivation.

 If you have taught or tutored before, you may collect the mistakes that your students made, then classify and analyze them. You may also develop a plan how you would apply your findings in your classroom.
Direction to be followed
1.Excluding the title and reference pages, your paper musthave at least 10 pages with double line space. Each missing page will result in a deduction of 15 points in addition to the deductions based on the following rubrics
2.(5 points) Professional appearance and format of your paper: The margins are not more than 1” from each side; the font size should not be larger than 12; and the fontcan be Calibri, or Times New Roman.  The paper must be numbered. The sizes of tables and picturesneed to be reasonable. Your paper should be organized in the following format:a.Project title, names of authors, emails and affiliations (optional)b.Project summary, abstract, and/or objectivesc.Project Body (you may use sections, bullets tables, pictures)d.Acknowledgement (if applicable)e.References:If you obtained any information from the Internet, include the URL.  Youneeduse the MLA (Modern Language Association) citation style, or the Chicago citation style, or the style of a reputable mathematical journal, for example, the Journal of Mathematical Analysis and Applications (http://www.elsevier.com/wps/find/journaldescription.cws_home/622886?generatepdf=true)
3 .(5 points) Summary or abstract of your project. You may include objectivestatements. a.Project title, namesof authors, emails,affiliations, abstract should be included in the title page

4. (15 points) Difficulty and complexity: There are four options for your project (see the next page). For Project Option 1 and 2, the difficulty refersto the level of school mathematics from the lowest, arithmetic,to the highest, calculus II. For Project Option 3, your project needs to be at least at the level you taught, teach, or will teach. The appropriatelength of the project is also a consideration of difficulty, thoughthe minimum length is 10 pages with double space. An unnecessarily lengthy paper will not be considered more difficult. Difficulty may mean complexity. Use and inclusion of definitions, theorems and proofs will reflect difficulty and complexity. The more difficult the mathematics is, the more points you may earn.
5. (15points) Originality or creativity: The first meaning of originality is that your paper must be your own work. Plagiarism is prohibited, and hence will resultin 0 for the entireproject. Anymaterials taken from the Internet, publications and other people’s work must be well cited. The second meaning of originality is that your work has not been seen on the Internet and in publications. Originality may also mean creativity. The more original work your project has, the more points you may earn.
6. (60 points) Readability and Communication: clear and correct calculation, derivation, proofs, applications and explanation; sufficient and appropriate examples; real world examples, particularly related to your students, school and community (this also contributesto originality); smooth connection and transition among concepts, definitions,theorems, examples, and explanations; use of pictures, diagrams, and tables; easiness for understanding; appropriate citation; completeness of the project; fun to read.

7.Correctness: mathematically your project must be correct. Errors and mistakes in mathematics will be subject to deduction of points you earn. Errors and mistakes inother areas (English, Education, Science…) may or may not cause a deduction, depending on the nature and significance of the errors andmistakes.
8.The instructor retains the final interpretation of the grading rubrics