V. Inferential Statistics

In statistics, we often rely on samples that are subsets of a larger data set. These samples help us make inferences or form assumptions about the larger data set. The larger data set is known as the population, and we draw elements or data from the population to form samples.

1. Populations    

   1) Definition of a population   

   2) Population data

2.  Sampling   

    1) Sample size   

    2) Simple random sampling   

    3) Stratified sampling  

VI. Probability

Probability is how certain we are that an event will or will not happen.  Probability values help us estimate the certainty of an event. An event with a probability value of 1 is extremely likely to happen, and a probability value of 0 is extremely unlikely to occur. Probabilities are assigned values within the range of from 0 to 1, and we compute probabilities using simple formulas. This section covers how we compute and interpret basic probability.

 1.  Independent events

      1) Probability of a single event

      2) Probability of two or more independent events both occurring

      3) Probability of equally likely outcomes

  2. Dependent events

     1) Probability of a single event

     2) Probability of either of two or more dependent events occurring

 VII. Hypothesis Testing

When we interpret the results of an experiment, we sometimes need to know if the findings are the result of the experiment or if they occurred by chance. Hypothesis testing is a statistical procedure for testing whether chance is a plausible explanation for an experimental result. We discover some basic methods to conduct a research experiment and test if the results are significant, or not significant due to chance.

1. Research statement

2. Hypothesis statement

    1) Null hypothesis

    2) Alternative hypothesis

3. Alpha level of significance

4. P-Value

5. Procedures to reject; or fail to reject the null hypothesis

VIII. Correlation

Correlation is a measure of the strength of the linear relationship between two variables. For example, 2 variables may be the relationship between gas mileage and vehicle maintenance. Correlation is the method we use to measure this relationship, and the correlation coefficient is the statistic that describes the strength of the relationship. We will discover how to use and interpret the correlation coefficient and apply the results for data analysis.

1.  Identifying linear relationships

2. Correlation coefficient

    1) Measure of strength of the linear relationship between 2 variables

    2) Symbol and values for the correlation coefficient

3. Independent and dependent variables

    1) Continuous variables

    2) strength of the negative or positive linear relationship