Notes, summaries, assignments, exams, and problems for Mathematics

1. The t-test is never valid if the sample size is small, say less than 30. (TRUE OR FALSE)

It can be valid if the sample is approximately normal.

2. The results of an observational study indicate that people who use vitamin supplements get fewer colds than people who don't. However, we can't conclude that vitamin supplements prevent colds because this type of study does not allow us to infer causation. (TRUE OR FALSE)

Only experimental designs can infer causation because it allows us to create treatment groups that are very similar.

3. A survey was administered to a random sample of college students. Both males and females were surveyed, and one question asked was "How much are you willing to spend on a stereo system (in dollars)?" An analysis

Polygon Interior Angles Theorem

The sum of the measures of interior angles of an n-gon is (n-2)x180

Interior angles of a quadrilateral:

The sum of the measures of the interior angles of a quadrilateral is 360^o

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Angles have to measure up to 360. 360/n (n=#of sides)

Theorems

If a quadrilateral is a parallelogram, then its opposite sides are congruent

If a quadrilateral is a parallelogram, then its opposite angles are congruent

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

If a quadrilateral is a parallelogram, then its diagonal bisects each other

If both pairs of opposite sides of a quadrilateral

Fm of citizens- 18,20,21. 1. Is an individual a citizen? 20. One doesn’t have to be economically active to rely on citizen rights, gained when born in the EU. 2. Measures to breach 21,18,20? Is there a right to reside restricted- 21, right of residence but can be limited by having sufficient resources. Right to not be discriminated on grounds of nationality- 18, once people have a residence permit, if not economically active can rely on 18 for social assistance. For students, request loans. MS- can request societal integration but do not require settled status, can find by demonstrating a period of time a student has been in the country. Broad breach- 20. 3. Does measures breach citizen rights on social advantage on 24.1 crd? a. Equal treatment... Continue reading "EU Citizenship Rights and Protections for Workers and Job Seekers" »

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What is Statistics?

Statistics is a set of tools designed to analyze data and deduce information about a population from a given sample.

The Three-Step Process of Statistics

1. Sampling and Design of the Experiment: Take a sample (or many) from the population, make observations about the sample, and turn them into numerical data.
2. Descriptive Statistics: Analyze the data to get information about the sample.
3. Statistical Inference: From the data, deduce information about the whole population.

Context is Crucial

The context of a statistical study is crucial in interpreting the results. A population is a set of individuals (people, cases, etc.) that we want to analyze. A sample is a subset of the population. A variable is an aspect or characteristic of the... Continue reading "Statistics: A Guide to Data Analysis and Population Inference" »

MONEY

Budgeting and Expenses

• Budget: A plan for how to spend money.
• Grant: Money given by the government for a particular purpose, often education.
• Loan: Money borrowed from a bank or other lender, usually with interest.
• Fee: Money paid for a professional service (e.g., lawyer, consultant).
• Fare: Money paid to travel by bus, train, taxi, etc.

Savings and Investments

• Savings: Money set aside for future use.
• Donation: Money given to a charity or other organization.
• Deposit: A portion of a larger payment made upfront.
• Will: A legal document that specifies how a person's assets will be distributed after their death.
• Lump sum: A single payment of a large amount of money.

Financial Terms

• Fine: Money paid as a penalty for breaking a rule or law.
• Installment: A

Decision Making and Problem Solving

Defining the Process

Problem Solving: Identifying the difference between the actual and desired state of affairs, and taking action to resolve the difference.

Decision Making: Defining the problem, identifying alternatives, determining criteria, evaluating alternatives, and choosing an alternative.

Types of Decision Problems

Single-Criterion Decision Problem: Finding the best solution based on one criterion.

Multicriteria Decision Problem: Finding the best solution considering multiple criteria.

Key Concepts in Decision Making

Decision: The selected alternative.

Model: A representation of a real object or situation.

• Iconic Model: A physical replica of a real object.
• Analog Model: A physical representation, but doesn'

Probability Distributions

Discrete Random Variables

1. If the outcomes of a discrete random variable follow a Poisson distribution, then which of the following is true?
   • (A) The mean equals the variance.
2. Which of the following is not a characteristic of a binomial probability distribution?
   • (A) Each trial has a finite number of possible outcomes.
3. If the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a binomial distribution and round the answer to four places.)
   • (C) 0.1800
4. The number of arrivals of delivery trucks per hour at a loading station is an example of which of the following processes?
   • (C) Poisson
5. When sampling without replacement

Standard Form/Scientific Notation

If you had a number like this:

54300000.0

Then you would have to make the number so it is under 10:

5.4300000

But you moved the decimal place 7 places to the left, so the standard form is:

5.43 x 10⁷

HINT

Recurring decimals are written with a little dot or a line above a number to show that it goes on forever.

HINT

Terminating decimals are decimals that eventually stop and are not recurring.

Rounding

When rounding, you round to the nearest number with the amount of decimal places provided. For example:

59.54

The critical digit (last number) determines what the number will be. In this example, the critical digit is 4. 4 or less, let it rest. 5 or more, raise the score. So because the critical digit is 4, you would round the... Continue reading "Decimals, Fractions, and Percentages" »

Apothem

The perpendicular distance from the center of a regular polygon to a side of the polygon.

Center of a Circle

The point inside a circle that is the same distance from every point on the circle.

Center of a Regular Polygon

The point that is equidistant from all vertices of a regular polygon.

Central Angle of a Regular Polygon

An angle whose vertex is the center of the regular polygon and whose sides pass through consecutive vertices.

Circle

The set of points in a plane that are a fixed distance from a given point called the center of the circle.

Composite Figure

A plane figure made up of triangles, rectangles, trapezoids, circles, and other simple shapes, or a three-dimensional figure made up of prisms, cones, pyramids, cylinders, and other simple... Continue reading "Geometry Terms and Definitions" »