Chi-Square Distribution
The Chi-Square Distribution, a fundamental concept in statistics, serves as a key tool for analyzing categorical data and evaluating the association between variables. Developed by Karl Pearson in the early 20th century, this probability distribution plays a pivotal role in hypothesis testing and goodness-of-fit assessments. Its distinctive shape and application in diverse fields, from biology to finance, underscore its universal significance in statistical inference. In this exploration, we will delve into the characteristics and applications of the Chi-Square Distribution, unraveling its relevance in the realm of statistical analysis.
Questions
- What is the shape of a chi-squared distribution?
- What determines the shape of a chi-square curve?
- What happens to the shape of a chi squared distribution as the number of degrees of freedom increases?
- What deterimines the number of degrees of freedom of a chi-squared distribution?
- How do you use the moment generating function of a chi-squared distribution to find the standard deviation?
- What is the probability density function of a chi-squared distribution?
- What is the cumulative distribution function of a chi-squared distribution?
- How does the chi-squared distribution relate to the Gamma distribution?
- What can a chi-squared distribution be used to describe?
- To find the 90% confidence interval for the population variance when n = 15 and the population is known to be normally distributed, what values of chi-squared would you use?