TERMS

• Z-table

  • Areas under the normal curve can be found using the
• Z-value (z-score)

  • is a measure of relative standing, with respect to the random variable X.
  • It represents the distance between a given measurement X and the mean, expressed in standard deviations.
• Steps in finding the areas under the normal curve with respect to a z-value:

  • Express the given z-value into a three-digit form(up to hundredths place).
  • Find the first two digits on the left column of the z-table.
  • Match the third digit with the appropriate column on the right.
  • Find the intersection of the row and the column
• Normal Random Variable

  • is a random variable that is called “normal” as a way of suggesting the depiction of a common or natural pattern that is observed in real life setting
• Normal Curve

  • is the graph of a normal random variable.
• Normal Distribution

  • is the probability distribution of a normal random variable.
• Standardizing

  • Raw scores may be composed of large values, but large values cannot be accommodated at the baseline of the normal curve.
  • So, you will convert any x-value of a normal distribution to its standard normal variable by using the z-score formula.
  • This process is known as-
• Population

  • is the totality of items, things, or people under consideration.
• Sample

  • is a subset of the population.
• Parameter (mean µ and standard deviation σ).

  • Any measurable characteristics of a population is called
• Statistic (mean x̄and standard deviation s)

  • Any measurable characteristic of a sample is called a
• Simple Random Sampling

  • is a selection of a subset of a population where each element has an equal chance of being selected.
• Sampling Erorr

  • The difference between the sample statistic and the population parameter is called the
• Sampling Distribution

  • The probability distribution of a statistic is called a
• Standard Error

  • The standard deviation of the sampling distribution is called the
• Sampling Distribution of Sample Means

  • is a probability distribution using the means computed from all possible random samples of a specific size taken from a population.
• Sampling Error

  • is a statistical error when a sample does not truly represent the population.
  • It is calculated by dividing the population standard deviation by the square root of the sample size then multiplied to a critical value (z or t).
• Sampling error

  • is derived from the standard error by multiplying it by z or t score to produce a confidence interval
• Margin of Error

  • is derived from the standard error by multiplying it to z or t score.
• Margin of error

  • is a statistical term that represents the range of uncertainty or variability around an estimate or measurement. It quantifies the degree of confidence we can have in the accuracy of the estimate.
• When is the CLT application?

  • If the sampled population is normal, then the CLT gives more than just an approximation.
  • If the sampled population is almost symmetric, the sampling distribution becomes approximately normal for relatively small values of n.
  • If the sample population is skewed, the sampling distribution becomes approximately normal only for large values of n. Usually, this is when 𝑛 ≥ 30.
• Central Limit Theorem

  • If random samples of size n are drawn from any population with a finite mean 𝜇 and a standard deviation 𝜎, n is large, the sampling distribution of the sample mean 𝑥ҧ is approximately distributed with mean 𝜇 and standard deviation

  
• Sample Space

  • set of all possible outcomes
  • usually denoted by a capital letter "s"
• Rule of Sum

  • if a particular action can be done in m ways and another in n ways, and the two actions cannot be done at the same time, then there are m + n ways of doing exactly of these actions
• Rule of Product

  • if a particular action can be done in m ways and another in n ways, then there are m × n ways of doing both actions (one after the other)
• Rule of Sum

  • is used for counting problems which involve several possibilities or actions, only one of which must occur at any given time
• Rule of Product

  • is used for tasks which involve several actions, all of which mist occur one after the other
• Permutation

  • different ways of counting
  • order is important
• Combination

  • arrangement of outcomes which order does not matter
• Probability

  • a measure of the likelihood of occurrences of an extent
• Random Variable

  • function or rule that assigns a number to each outcome of a experiment
  • in general, a random variable is denoted by x
  • it can be discrete or continuous
• Discrete Random Variable

  • the result is whole number
  • value is obtained by counting
• Continuous Random Variable

  • result is decimal or faction
  • value is obtained by measuring
• Measures of Central Tendency

  • summary statistics that represents the center point or typical value of a data set
• Measure of Variablity

  • summary statistics that represent the amount of dispersion in a dataset
• Mean (Expected Value)

  • the theoretical average of the variable
  • its expected value is the long-run average value of x
• Variance

  • describes how much a random variable differs from its expected value
• Coefficient of Variation

  • a measure of relative dispersion that expresses the standard deviation as a percentage of the mean
• Standard Deviation

  • square root of variance
• Normal Distribution

  • continuous random variable has a bell shaped probability distribution also known as normal variable and its probability
  • often called the bell curve because the graph of its probability distribution looks like a bell
  • also known as Gaussian Distribution, after the german mathematician Carl Friedrich Gauss who first described it