STATS 4TH QTR

Continuous Random Variable

Has an infinite number of possible values that can be represented by an interval on the number line.

Continuous Probability Distribution

The probability distribution of a continuous random variable.

Normal Distribution

• A continuous probability distribution for a random variable, x.

• The most important continuous probability distribution in statistics.

• The graph of a normal distribution is called the normal curve.

Properties of Normal Distribution

• The mean, median, and mode are equal.

• The normal curve is bell-shaped and symmetric about the mean.

• The total area under the curve is equal to one.

• The normal curve approaches, but never touches the x-axis as it extends farther and farther away from the mean.

Properties of Normal Distribution

The area under the part of normal curve that lies within:

• 1 standard deviation of the mean is approximately 0.68 or 68%;

• within 2 standard deviations, about 0.95 or 95%; and

• within 3 standard deviations, about 0.997 or 99.7%

Means and Standard Deviations

• A normal distribution can have any mean and any positive standard deviation.

• The mean gives the location of the line of symmetry.

• The standard deviation describes the spread of the data

Standard Normal Distribution

• 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: z = x - mean / o

• The result if each data value of a normally distributed random variable x is transformed into a z-score.

Properties of Standard Normal Distribution

• The cumulative area is close to 0 for z-scores close to z = -3.49.

• The cumulative area increases as the z-scores increase.

Population

A complete collection, or set, of individuals or objects or events whose properties are to be analyzed. (PARAMETER)

Sample

A sub collection of members selected from a population. (STATISTIC)

Survey

• Gathering info/data from target sample for quantitive descriptors

• Ex: Telephone survey, mailed questionnaire, personal interview

Census

• To gather data from every member (individual)

• Small population/entire population is needed

Slovin’s Formula

n = N / 1 + Ne²

• N = population

• n = sample

• e = margin of error (5% / 0.05)

Sampling

• Predetermined number of observations/samples from population

• Who/what will be a part of your sample

Probability Sampling

• Each individual has a non-zero probability of being selected (chance to be selected for sample)

• Random selection

Non-Probability Sampling

• Non-random method, selected based on convenience/preference/other data.

• Easily collected but biased

Random Sampling Technique

• All members have equal changes for selection

• The purest form

• Uses numbers (ex: give every individual a number, choose specific numbers/range of numbers) — Table of Random Numbers

Systematic Sampling Technique

• Arranging target according to a specific order

• Random start to every kth element from then onwards (Ex: 50th — 50, 100, 150, 200..)

• kth interval = popu size / samp size

Stratified Sampling Technique

• Dividing population into stratas, then randomly pick

• For large populations

• Specific number, not all

• Ex: Identify total per section (population = grd 11), how many samples per strata (by section)

Sampling

A process used in statistical analysis in which a predetermined number of observations are taken from a larger population.

Probability Sampling

• Each member of the population has a known non-zero probability of being selected.

• Involves random selection, allowing you to make strong statistical inferences about the whole group.

Non-Probability Sampling

• Members are selected from the population in some nonrandom manner.

• Involves non-random selection based on convenience or other criteria, allowing you to easily collect data.

Cluster Sampling Technique

Dividing population into clusters then select 1 or more clusters by random and use ALL selected members in the sample.

Sampling Distribution

Is a distribution that describes the probability for each mean of all samples with the same sample size n.