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Population

Entire group under study, which can be finite, infinite, real, or hypothetical.

Sample

Subset of the population used for analysis.

Sample Size

Number of elements in the sample.

Sampling Methods

Techniques like random or stratified sampling used to ensure representativeness.

Mean of Sampling Distribution

Equals population mean, denoted as \mu_{\bar{X}} = \mu.

Standard Error (SE)

Calculated as \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}, decreases as n increases.

Central Limit Theorem (CLT)

States that for n \geq 30, the sampling distribution of \bar{X} is approximately normal.

Point Estimate

Single value used to estimate a population parameter, such as \bar{x} for \mu.

Interval Estimate

Range of values with a confidence level, such as a 95% confidence interval.

Margin of Error

Calculated as Z_{\alpha/2} \times \text{SE}.

CI for Mean (when \sigma is known)

Expressed as \bar{x} \pm Z_{\alpha/2} \frac{\sigma}{\sqrt{n}}.

CI for Mean (when \sigma is unknown)

Use t-distribution for small samples (n < 30).

Regression

Models the relationship between dependent ($Y$) and independent ($X$) variables.

Regression Equation

Expressed as Y = a + bX.

Slope (b)

Calculated as b = \frac{\sum (xi - \bar{x})(yi - \bar{y})}{\sum (x_i - \bar{x})^2}.

Intercept (a)

Calculated as a = \bar{y} - b\bar{x}.

Correlation (Pearson’s r)

Measures the strength of linear relationship, ranging from -1 to 1.

Perfect Positive Correlation (r = 1)

Indicates a perfect positive linear relationship between variables.

Perfect Negative Correlation (r = -1)

Indicates a perfect negative linear relationship between variables.

No Correlation (r = 0)

Indicates no linear relationship between variables.

Time Series Analysis

Sequence of numbers collected at a regular interval over a period of time

Secular Trend

Long-term direction in time series data.

Seasonal Variation

Periodic fluctuations in data over specific intervals.

Cyclical Variations

Fluctuations that occur in economic cycles.

Irregular Variation

Random noise in time series data.

Least Squares Method

A technique used to fit a trend line in time series analysis.

Moving Average

Method that smooths data to highlight trends.

Standard Error Formula

\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}.

Correlation Coefficient Formula

r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}.

Hypothesis testing

Used to test a hypothesis about a population based on sample data

Correlation

A measure that describes the strength and direction of the relationship between two variables

Regression

Method used to model the relationship between variables, helps predict value based on the value of another

Descriptive statistics

It summarises and describes the main features of a dataset eg averages and variables

Estimation

Uses sample data to infer population parameters

Point estimation

Single value estimate of a parameter

Interval estimate or confidence interval

Range within which the parameters like fall

Population

Entire group under study, which can be finite, infinite, real, or hypothetical.

Sample

Subset of the population used for analysis.

Sample Size

Number of elements in the sample.

Sampling Methods

Techniques like random or stratified sampling used to ensure representativeness.

Mean of Sampling Distribution

Equals population mean, denoted as \mu_{\bar{X}} = \mu.

Standard Error (SE)

Calculated as \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}, decreases as n increases.

Central Limit Theorem (CLT)

States that for n \geq 30, the sampling distribution of \bar{X} is approximately normal.

Point Estimate

Single value used to estimate a population parameter, such as \bar{x} for \mu.

Interval Estimate

Range of values with a confidence level, such as a 95% confidence interval.

Margin of Error

Calculated as Z_{\alpha/2} \times \text{SE}.

CI for Mean (when \sigma is known)

Expressed as \bar{x} \pm Z_{\alpha/2} \frac{\sigma}{\sqrt{n}}.

CI for Mean (when \sigma is unknown)

Use t-distribution for small samples (n < 30).

Regression

Models the relationship between dependent ($Y$) and independent ($X$) variables.

Regression Equation

Expressed as Y = a + bX.

Slope (b)

Calculated as b = \frac{\sum (xi - \bar{x})(yi - \bar{y})}{\sum (x_i - \bar{x})^2}.

Intercept (a)

Calculated as a = \bar{y} - b\bar{x}.

Correlation (Pearson’s r)

Measures the strength of linear relationship, ranging from -1 to 1.

Perfect Positive Correlation (r = 1)

Indicates a perfect positive linear relationship between variables.

Perfect Negative Correlation (r = -1)

Indicates a perfect negative linear relationship between variables.

No Correlation (r = 0)

Indicates no linear relationship between variables.

Time Series Analysis

Sequence of numbers collected at a regular interval over a period of time

Secular Trend

Long-term direction in time series data.

Seasonal Variation

Periodic fluctuations in data over specific intervals.

Cyclical Variations

Fluctuations that occur in economic cycles.

Irregular Variation

Random noise in time series data.

Least Squares Method

A technique used to fit a trend line in time series analysis.

Moving Average

Method that smooths data to highlight trends.

Standard Error Formula

\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}.

Correlation Coefficient Formula

r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}.

Hypothesis testing

Used to test a hypothesis about a population based on sample data

Correlation

A measure that describes the strength and direction of the relationship between two variables

Regression

Method used to model the relationship between variables, helps predict value based on the value of another

Descriptive statistics

It summarises and describes the main features of a dataset eg averages and variables

Estimation

Uses sample data to infer population parameters

Point estimation

Single value estimate of a parameter

Range within which the parameters like fall