Descriptive Statistics, Probability, and Regression Analysis

This assignment delves into the core concepts of statistics, encompassing descriptive statistics, probability, and regression analysis. It provides a comprehensive overview of descriptive statistics, including measures of central tendency (mean, median, mode) and dispersion (standard deviation, quartiles). The assignment also explores probability distributions like binomial and Poisson, along with the normal distribution. Furthermore, it covers linear regression analysis, including the calculation of the product moment correlation coefficient. Additionally, it includes tests such as Chi-Square and confidence intervals for both population means and proportions. The assignment concludes with a discussion of hypothesis testing and the calculation of test statistics for various scenarios. This resource aims to provide a solid foundation in statistical methods and their applications.

DESCRIPTIVE STATISTICS
Mean and Standard Deviation for Raw Data
Sample mean
Population standard deviation
Sample standard deviation
where observation; number of observations
Mean and Standard Deviation for Grouped Data
Sample mean
Population standard deviation
Sample standard deviation
where class frequency; class midpoint
Quartile Deviation
where upper quartile; lower quartile
Pearson Measure of Skewness
or

Median
where median class lower bound; median class frequency;
median class width; total number of observations;
sum of all frequencies before the median class
Mode
where modal class lower bound; modal class frequency;
modal class width;
frequency of class before modal class;
frequency of class after modal class
INDEX NUMBERS
Price Quantity
Laspeyres
Paasche
where base period price; base period quantity;
current period price; current period quantity
PROBABILITY

PROBABILITY DISTRIBUTION
BINOMIAL DISTRIBUTION
If ~ then
POISSON DISTRIBUTION
If ~ then
NORMAL DISTRIBUTION
LINEAR REGRESSION ANALYSIS
Linear Regression Equation
where
Product Moment Correlation Coefficient
CHI-SQUARE TEST

where observed frequencies; expected frequencies
CONFIDENCE INTERVAL
When population variance is known, confidence interval for is:
When population variance is unknown and confidence interval
for is:
When population variance is unknown and confidence interval
for is:
TEST STATISTICS
For Mean
When population variance is known,
When population variance is unknown and
When population variance is unknown and
Where sample size; population standard deviation;
population mean; estimator for ;
sample mean
For Proportion

Where sample proportion; population proportion; sample size
For Paired Sample
where the mean of estimator for
sample size
For Difference of Two Means
When population variances are known,
When population variances are unknown,
for and
or for and
where sample size 1; sample size 2;
sample mean 1; sample mean 2;
population mean 1; population mean 2;
population variance 1; population variance 2;
sample variance 1; sample variance 2;
pooled estimator for