In at least 250 words explain how would you get data to test

In at least 250 words explain how would you get data to test a hypothesis.

Solution

Hypothesis Testing:

The second type of inference method - confidence intervals was the first, is hypothesis testing. A hypothesis, in statistics, is a statement about a population where this statement typically is represented by some specific numerical value. In testing a hypothesis, we use a method where we gather data in an effort to gather evidence about the hypothesis. In hypothesis testing there are certain steps one must follow. Below these are summarized into six such steps to conducting a test of a hypothesis.

1. Setting up two competing hypotheses - Each hypothesis test includes two hypothesis about the population. One is the null hypothesis, notated as H_o, which is a statement of a particular parameter value. This hypothesis is assumed to be true until there is evidence to suggest otherwise. The second hypothesis is called the alternative, or research, hypothesis, notated as H_a. The alternative hypothesis is a statement of a range of alternative values in which the parameter may fall. One must also check that any assumptions (conditions) needed to run the test have been satisfied e.g. normality of data, independence, and number of success and failure outcomes.

2. Set some level of significance called alpha. This value is used as a probability cutoff for making decisions about the null hypothesis. As we will learn later, this alpha value represents the probability we are willing to place on our test for making an incorrect decision in regards to rejecting the null hypothesis. The most common alpha value is 0.05 or 5%. Other popular choices are 0.01 (1%) and 0.1 (10%).

3. Calculate a test statistic. Gather sample data and calculate a test statistic where the sample statistic is compared to the parameter value. The test statistic is calculated under the assumption the null hypothesis is true, and incorporates a measure of standard error and assumptions (conditions) related to the sampling distribution. Such assumptions could be normality of data, independence, and number of success and failure outcomes.

4. Calculate probability value (p-value), or find rejection region - A p-value is found by using the test statistic to calculate the probability of the sample data producing such a test statistic or one more extreme. The rejection region is found by using alpha to find a critical value; the rejection region is the area that is more extreme than the critical value.

5. Make a test decision about the null hypothesis - In this step we decide to either reject the null hypothesis or decide to fail to reject the null hypothesis. Notice we do not make a decision where we will accept the null hypothesis.

6. State an overall conclusion - Once we have found the p-value or rejection region, and made a statistical decision about the null hypothesis (i.e. we will reject the null or fail to reject the null). Following this decision, we want to summarize our results into an overall conclusion for our test.

Hypotheses and Test Statistics

We will continue our discussion by considering two specific hypothesis tests: a test of one proportion, and a test of one mean. We will provide the general set up of the hypothesis and the test statistics for both tests. From there, we will branch off into specific discussions on each of these tests.

In order to make judgment about the value of a parameter, the problem can be set up as a hypothesis testing problem.

The Null and Alternative Hypothesis

We usually set the hypothesis that one wants to conclude as the alternative hypothesis, also called the research hypothesis.

There are three types of alternative hypotheses:

1. The population parameter is not equal to a certain value. Referred to as a \"two-sided test\".

2. The population parameter is less than a certain value. Referred to as a \"left-tailed test\"

3. The population parameter is greater than a certain value. Referred to as a \"right-tailed test\".

For all three alternatives, the null hypothesis is the population parameter is equal to that certain value.