statistcs chapter 7-9

Confidence Interval

A range of values used to estimate the true value of a population parameter.

Sampling Error

Variation in results that occurs due to the randomness of the sample taken from a population.

Point Estimate

A single value statistic that serves as a best guess or approximation of a population parameter.

Standard Deviation (SD)

A measure of the amount of variation or dispersion in a set of values.

Standard Error

The standard deviation of the sampling distribution of a statistic, typically the sample mean.

Null Hypothesis (H0)

The hypothesis that there is no effect or no difference; it is the default assumption.

Alternative Hypothesis (Ha)

The hypothesis that indicates the presence of an effect or a difference; what is being tested.

Type 1 Error

Rejecting a true null hypothesis; also known as a false positive.

Type 2 Error

Failing to reject a false null hypothesis; also known as a false negative.

Z-Statistic

A statistic used in hypothesis testing that indicates how many standard deviations an element is from the mean when the population standard deviation is known.

T-Statistic

A statistic used in hypothesis testing that indicates how many standard deviations the sample mean is from the population mean when the population standard deviation is unknown.

Margin of Error

The amount of error that is allowed in a statistical estimate.

Degrees of Freedom

The number of independent values or quantities that can vary in an analysis without violating any constraints.

Confidence Level

The percentage of the population that the confidence interval is expected to include, typically expressed in percentages like 90%, 95%, or 99%.

Hypothesis Testing

A method of making statistical decisions using experimental data.

Power of the Test

The probability that the test correctly rejects a false null hypothesis.

Estimation

The process of inferring the value of a population parameter based on sample data.

Z Table

A table that provides the area (or probability) associated with a standard normal distribution for different Z-values.

T Table

A table that provides the critical values of the T-distribution for different degrees of freedom.

Statistically Significant

A term applied when observed results are unlikely to have occurred by chance, typically measured at a threshold of 0.05.

Sample Size (n)

The number of observations in a sample.

Population Parameter

A characteristic or measure obtained by using all the data values from a specific population.

Bootstrapping

A resampling method that allows estimation of the sampling distribution of a statistic by sampling with replacement.

Confidence Interval Calculation Steps

Steps to calculate confidence intervals include converting percentage to decimal, calculating margin of error, and determining bounds.