2MATHMWORLD - MIDTERM REVIEWER

Normal Space Distribution

it is a normal distribution with a mean of 0 and a standard deviation of 1. Any x-value can be transformed into a z-score by using the formula.

Hypothesis

is a statement about concepts that refers to observable phenomena which may be judged as true or false and is subject to empirical testing.

Directional Hypothesis

are those where one can predict the direction (effect of one variable on the other as “Positive” or “Negative”). For example, Girls perform better than boys (“better than” shows the direction predicted). A celebrity endorser will lead to increased sales for the product.

Non-Directional Hypothesis

are those where one does not predict the kind of effect but can state a relationship between variable 1 and variable 2. For example, there will be a difference in the performance of girls and boys (Not defining what kind of difference).

Null Hypothesis

is a statistical hypothesis that contains a statement of equality such as ≤, =, or ≥.

Alternate Hypothesis

is the complement of the null hypothesis. It is a statement that must be true if H_o is false and contains a statement of inequality such as >, ≠, <.

Type 1 Error

occurs if the null hypothesis is rejected when it is true.

Type 2 Error

occurs if the null hypothesis is not rejected when it is false.

Level of Significance

is the maximum value of the probability of rejecting the true null hypothesis. It is denoted by α the lowercase Greek letter alpha.

Test Statistic

The statistic that is compared with the parameter in the null hypothesis. After stating the null and alternative hypotheses and specifying the level of significance, a random sample is taken from the population and sample statistics are calculated.

Left-Tailed Test

If the alternative hypothesis contains the less-than inequality symbol (<), the hypothesis test is a left-tailed test.

H_o: μ ≥ k

H_a: μ < k

Right-Tailed Test

If the alternative hypothesis contains the greater-than symbol >, the hypothesis test is a right-tailed test.

H_o: μ ≤ k

H_a: μ > k

One-Tailed Test

When the critical region is located at only one extreme distribution or range of values for the test statistic.

Two-Tailed Test

if the alternative hypothesis contains the not-equal-to symbol (≠), the hypothesis test is a two-tailed test. In a two-tailed test, each tail has an area of 1P2.

H_o: μ = k

H_a: μ ≠ k

Z-Test

is a statistical test for a population mean. The z-test can be used when the population is normal and is known, or for any population when the sample size n is at least 30.

Statistics

A branch of mathematics that deals with collecting, organizing, analyzing, interpreting, and presenting data.

Nominal Data

Numbers and names that are used to classify data without particular ranking. Type of data that is used to label or categorize without any quantitative value. Example: Gender male and female, colors- red, blue etc, product codes ( abc123), password, username.

Ordinal Data

Numbers are used to indicate rank or order but the differences between the ranks are not equal or measurable. Example: Taste test ranking of three brands of soft drink- very satisfied, very satisfied, not satisfied. Position within an organization, 1 for President, 2 for Vice President, 3 for Plant Manager, 4 for Department Supervisor, 5 for Employee.

Interval Data

Quantitative data with equal intervals between consecutive values. No True “0” starting point Examples: Temperature in Celsius or Fahrenheit ( 20⁰C, 25⁰C, 30⁰C) 30⁰ C doesn’t mean no temperature, IQ.

Ratio Data

Highest level of measurement. Quantitative data with equal intervals. Has true zero point means the absence of the attribute being measured. Examples: Height, Weight, and Volume, the difference between 10 kg and 20 kg is the same as the difference between 20 kg and 30 kg. 20 kg is twice as heavy as 10kg

Population

the whole. A collection of persons, objects, or items under study.

Census

gathering data from the entire population.

Sample

a portion of the whole. A subset of the population. Its purpose is to draw the inference about the population.

Descriptive Statistics

used to say something or describe a set of information collected. It can also be represented by graphs. It involves methods of organizing ,picturing, and summarizing samples or population. For example, mean , median , mode , standard deviation. In an English test , 45 out of 50 students passed the exam. The median score in the first grading test of 50 students is 35. Expenses of ABC Company were 15 million in 2011.

Inferential Statistics

branch of statistics aims to give information about a larger group (population) using information collected from a small part of that population ( sample). It involves methods concerned with the analysis of a sample data leading to prediction or conclusion about the entire population.  Drinking wine may reduce the risk of heart diseases by 12 %. A prediction has been made that the chance that a person will be robbed in a certain city is 15%. There is a difference between smoking cigarettes and getting emphysema.

Parameter

any data obtained from the population.  Usually represented by Greek letters.

Statistic

any measure obtained from a sample. Usually represented by Roman letters.

Qualitative Data

It is the description of data in a language rather than in numbers. It is also sometimes referred to as categorical data . It only deals with data that can be observed like texture, taste, smell, beauty, but not measured.

Quantitative Data

Is a method in which data can be numerically counted . It is represented by histograms, tables, charts , and graphs. It deals with measurements like weight, volume, area , temperature or class size, tuition fee, no. of teachers etc.

Discrete Data

is numeric data in which the values can come only from a list of specific values. Discrete data results from a counting process.ex, the number of students in a class, results of rolling 2 dice

Continuous Data

is numeric data that can take on values at every point over a given interval. Continuous data result from a measuring process. Ex. A dog’s weight, the length of a leaf etc.

Sampling

is the process of selecting observations ( a sample) to provide an adequate description and inferences about the population.

Probability Sampling

all persons have a chance of being selected and results are more likely to accurately reflect the entire population.

Non-Probability Sampling

not all persons have a chance of being selected.

Simple Random Sampling

is the method of selecting a sample size (n) from a universe (N) such that each number of the population has an equal chance of being selected at the sample.

Systematic Sampling

individuals are selected at regular intervals from the sampling frame. Then every nth number on the list is selected.

Stratified Sampling

in this method the population is divided into two or more groups called strata. Subsample are randomly selected from each strata.

Cluster Sampling

the population is divided into subgroups (clusters) like i a community. A simple random sample is taken from each cluster.

Purposive Sampling

also known as judgmental, selective, or subjective sampling is a form of non-probability sampling . It is used when respondents are chosen for the reason that they possess the characteristic/s that the researcher is interested in.

Convenience Sampling

involves choosing respondents at the convenience of the researcher.

Snowball Sampling

also known as chain-referral sampling. The researcher starts with a key person and introduces the next one to become a chain.

Collection of Data

It is the first step in conducting a study or research after the formulation of the research problem.  It is the compilation and interpretation of primary and secondary sources of information. The integration of different sources will consolidate the write up of the report. 

Primary Data

are firsthand information. Information gathered directly from the source. Data from government institutions, business agencies, and other organizations Data from personal interviews.

Secondary Data

Data that has been collected for another purpose. Data from books, encyclopedias, journals, magazines, and other research or studies conducted by other individuals.

Problem Solving

engaging in a task for which the solution method is not known in advance. In order to find a solution , students must draw on their knowledge and through this process , they will often develop new mathematical understanding. Solving a problem is not only a goal of knowing mathematics , but also a major means of doing so. It encompasses exploring, reasoning, strategizing, estimating, conjecturing, testing, explaining , and proving.

Problem

the task that requires the learner to reason through a situation that will be challenging but not impossible.

George Polya

One of the recent mathematicians who outlined a strategy for solving problems. He is considered the father of problem solving among mathematicians.

Inductive Reasoning

It is characterized by drawing conclusions or conjecture from repeated observation of specific examples . A conjecture is an idea that may or may not be correct.

Deductive Reasoning

applying general principles to specific examples.