Chapter 8
Distributions
Distributions to Estimate Population Parameter
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually ...
Degrees of Freedom
The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent ...
Student t Distribution
The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the ...
Choosing Between z and t Distribution
The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to ...
Chi-square Distribution
How does one determine if bingo numbers are evenly distributed or if some numbers occurred with a greater frequency? Or if the types of movies people ...
Finding Critical Values for Chi-Square
Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to ...
Estimating Population Standard Deviation
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of ...
Goodness-of-Fit Test
The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may ...
Expected Frequencies in Goodness-of-Fit Tests
A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the ...
Contingency Table
A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution ...
Introduction to Test of Independence
In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their ...
Hypothesis Test for Test of Independence
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test ...
Determination of Expected Frequency
Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of ...
Test for Homogeneity
The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two ...
F Distribution
The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of ...
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