STEPS FOR PERFORMING A SIGNIFICANCE TEST
A hypothesis is a statement about the population. A significance test is a method for using data to summarize the evidence about a hypothesis. The null hypothesis (H0) is a statement that the parameter takes a particular value (e.g: probability of getting a baby girl: p = 0.482). The alternative hypothesis (Ha) states that the parameter falls in some alternative range of values. A significance test has five steps:

1. Assumptions
   Each significance test has certain assumptions or has certain condition under which it applies (e.g: an assumption is the assumption that random sampling has been used).
2. Hypotheses
   Each significance test has two hypotheses about a population parameter. The null hypothesis and the alternative hypothesis.
3. Test statistic
   The parameter to which the hypotheses refer has a point estimate. A test statistic describes how far that

HOW SAMPLE PROPORTIONS VARY AROUND THE POPULATION PROPORTION
The sample distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. The population distribution from which you take the sample. Values of its parameters are fixed, but usually unknown. Data distribution is the distribution of the sample data. It is also called sample proportion. Sampling distribution is the distribution of a sample statistic such as a sample proportion. Sampling distributions describe the variability that occurs from sample to sample.

For a random sample size n from a population with proportion p of outcomes in a particular category, the sampling distribution of the sample proportion in that category has:

 and 

For a large sample size n, the binomial distribution has a normal distribution. The central limit

THE ASSOCIATION BETWEEN TWO CATEGORICAL VARIABLES
When analysing data the first step is to distinguish between the response variable and the explanatory variable. The response variable is the outcome variable on which comparisons are made. If the explanatory variable is categorical, it defines the groups to be compared with respect to values for the response variable. If the explanatory variable is quantitative, it defines the change in different numerical values to be compared with respect to values for the response variable. The explanatory variable should explain the response variable (e.g: survival status is a response variable and smoking status is the explanatory variable).

An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable.

A contingency table is a display for two categorical variables. Conditional proportions are proportions which formation

DIFFERENT TYPES OF DATA
A variable is any characteristic observed in a study. The data values that we observe for a variable are called observations. A variable can be categorical and quantitative.

• Categorical variables are variables that belong to a distinct set of categories. A categorical variable can be numerical, because some variables do not vary in quantity. (e.g: religion, favourite sport, bank account, area codes)
• Quantitative variables are variables that have numerical values and represent different magnitudes. (e.g: weight, height, hours spent watching TV every day)

Key features to describe quantitative variables are the centre and the variability (spread) of the data (e.g: average amount of hours spent watching TV every day). Key feature to describe categorical variables is the relative number of observations in various categories. (e.g: the percentage of days in a year that it was sunny)

Quantitative