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Activity 6

Section 5: Hypothesis Testing, T-Tests, Cross-Tabulation Tables and Chi-Square Test

The content covered in this section includes; Hypothesis Testing, T-Tests, Cross-Tabulations, and Chi-Square test. The difference between a null and alternative hypothesis and how to set up the hypothesis (the specific symbolic components that are often used in testing hypotheses) will be covered in detail. Student will have the opportunity to explore the difference between one- and two-tailed testing and understand the importance of the P-value for setting up proper hypothesis testing. Type I and Type II errors should be understood in the context of hypothesis testing and how increasing or decreasing the level of rejection can lead to greater levels of certain types of errors.

The second part of this section is an introduction to cross-tabulations, Chi-Square test, t-tests, and One-Way ANOVA parametric and nonparametric measures. Importance is placed on calculating these tests through the use of statistical software, as well as analyzing and interpreting their results. In addition to manipulating computations, the conceptual basis of each test will be explored.

Hypothesis Testing (also called "significance testing") is a statistical procedure for discriminating between two statistical hypotheses; the null hypothesis (H₀) and the alternative hypothesis ( H_a, often denoted as H₁). Hypothesis testing rests on the presumption of validity of the null hypothesis; the null hypothesis is rejected only if the data at hand testify strongly enough against it. The philosophical basis for hypothesis testing rests in the fact that random variation pervades all aspects of life and in the desire to avoid being fooled by what might be chance variation.

A t-test is a statistical hypothesis test based on a test statistic whose sampling distribution is a t-distribution. Various t-tests are aimed at testing hypotheses about populations with normal probability distribution. However, t-tests often provide adequate results for non-normally distributed populations. The most popular t-tests are aimed at testing the following hypotheses:

1) The population mean is as hypothesized (the population variance is not known).

2) The means of two populations are equal (the population variances are not known but equal).

3) The means of two populations are equal (the population variances are not known and not equal).

4) The correlation coefficient for two random variables is zero.

5) The slope of the population regression line is zero.

A cross-tabulation table represents the joint frequency distribution of two discrete variables. Rows and columns correspond to the possible values of the first and the second variables, the cells contain frequencies (numbers) of occurrence of the corresponding pairs of values of the 1st and 2nd variable. Cross-tabulation tables can be used for more than two variables.
Chi-square test (or

test) is a statistical test for testing the null hypothesis that the distribution of a discrete random variable coincides with a given distribution.

Analysis of Variance (ANOVA) is a statistical technique which helps in making inference whether three or more samples might come from populations having the same mean; specifically, whether the differences among the samples might be caused by chance variation.

Required Reading:

Please refer to each Activity for required readings.

Assignment 6 Paper � Testing the Hypothesis

In the world of research there are facts and opinions; however, reviewing the data presented and making the distinction of such is essential. Many promoters will provide claims to support a product or stance. Regardless of the topic and either a positive or negatives perspective shared, statistics offers a way to test and verify many claims through a set of techniques called hypothesis testing. Hypothesis testing which is also known as significance, testing is a statistical procedure for discriminating between two statistical hypotheses; (a) the null hypothesis (H₀) and (b) the alternative hypothesis (H_a, often denoted as H₁). Hypothesis testing relies upon the presumption of validity of the null hypothesis, which is rejected only if the data at hand testify strongly enough against it. The null hypothesis stands ("is not rejected") unless the data at hand provide strong enough evidence against it. "Strong enough" means that the probability that you would obtain a result as extreme as the observed result, given that the null hypothesis is true, is small enough (usually < 0.05) given the null hypothesis is true.

Assignment Preparation

1. Read Chapter 9 in the following primary course resource: Statistical reasoning for everyday life.

2. Supplemental Video Lectures

Hypothesis Testing, Part 1	http://youtu.be/rHAxhlmbRPU
Hypothesis Testing, Part 2	http://youtu.be/kMxDtJL3RFY
Example of Hypothesis Testing: Two-Tail Test	http://youtu.be/3IuXVDm3NXY
Hypothesis Testing and P-values	http://youtu.be/-FtlH4svqx4

The unit readings are critical as they introduce and explain the concepts of hypothesis testing. By the completion of this unit, you should gain proficiency in understanding and applying the following concepts and processes:

(a) Fundamentals of Hypothesis Testing

(b) Hypothesis Tests for Population Means

Main Task: Test Your Hypothesis
In this activity, students are asked to design a hypothesis test, collect data, analyze the data and share a conclusion. The focus may be something used in everyday life and general in nature.

Assignment requirements:

(a) Clearly identify the objective of your test.

(b) Clearly identify what the conditions, your hypotheses, and your rejection criteria.

(d) Analyze the data and share an appropriate descriptive statistics of your samples.

(e) Calculate test the test statistics and rejection criteria.

(f) Clearly share your conclusion and opinion.

Length: 5-7 pages