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# BNAD277 Chapter 9 Notes BNAD277

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This 4 page Class Notes was uploaded by Kristin Koelewyn on Thursday February 25, 2016. The Class Notes belongs to BNAD277 at University of Arizona taught by Dr. S. Umashankar in Spring 2016. Since its upload, it has received 44 views. For similar materials see Business Statistics in Business at University of Arizona.

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Date Created: 02/25/16

Bnad277: Chapter 8 Notes Hypothesis Testing: - Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected. - The null hypothesis, denoted by H ,0is a tentative assumption about a population parameter. - The alternative hypothesis, denoted by H , as the opposite of what is stated in the null hypothesis. - The hypothesis testing procedure uses data from a sample to test the two competing statements indicated by H an0 H . a - Developing a Null and Alternative Hypotheses: o Many applications of hypothesis testing involve an attempt to gather evidence in support of a research hypothesis. o In such cases, it is often best to begin with the alternative hypothesis and make it the conclusion that the researcher hopes to support. o The conclusion that the research hypothesis is true is made if the sample data provide sufficient evidence to show that the null hypothesis can be rejected. o It is not always obvious how the null and alternative hypotheses should be formulated. o Care must be taken to structure the hypotheses appropriately so that the test conclusion provides the information the researcher wants. o The context of the situation is very important in determining how the hypotheses should be stated. o In some cases it is easier to identify the alternative hypothesis first. In other cases the null is easier. o Correct hypothesis formulation will take practice. o Summary: ▯ The equality part of the hypotheses always appears in the null hypothesis. ▯ In general, a hypothesis test about the value of a population mean m must take one of the following three forms (where m 0s the hypothesized value of the population mean). ▯ - Type 1 Error: o Because hypothesis tests are based on sample data, we must allow for the possibility of errors. o A Type I error is rejecting H wh0n it is true. o The probability of making a Type I error when the null hypothesis is true as an equality is called the level of significance. o Applications of hypothesis testing that only control the Type I error are often called significance tests. - Type 2 Error: o A Type II error is accepting H whe0 it is false. o It is difficult to control for the probability of making a Type II error. o Statisticians avoid the risk of making a Type II error by using “do not reject H 0 and not “accept H ”. 0 - P value Approach to One-Tailed Hypothesis Testing: o The p-value is the probability, computed using the test statistic,that measures the support (or lack of support) provided by the sample for the null hypothesis. o Reject H if0the p-value < a. - Steps of Hypothesis Testing: o Step 1. Develop the null and alternative hypotheses. o Step 2. Specify the level of significance a. o Step 3. Collect the sample data and compute the value of the test statistic. o Step 4. Use the value of the test statistic to compute the p-value. o Reject H if 0-value < a. - P Value Approach to Two-Tailed Hypothesis Testing: o 1. Compute the value of the test statistic z. o 2. If z is in the upper tail (z > 0), compute the probability that z is greater than or equal to the value of the test statistic. If z is in the lower tail (z < 0), compute the probability that z is less than or equal to the value of the test statistic. o 3. Double the tail area obtained in step 2 to obtain the p –value. o 4. Reject H if0the p-value < a . - Tests About a Population Mean: o Test Statistic: ▯ This test statistic has a t distribution with n - 1 degrees of freedom. - P -Values and the t Distribution: o The format of the t distribution table provided in most statistics textbooks does not have sufficient detail to determine the exact p- value for a hypothesis test. o However, we can still use the t distribution table to identify a range for the p-value. o An advantage of computer software packages is that the computer output will provide the p-value for the t distribution. - Summary of Forms for Null and Alternative Hypotheses About a Population Proportion: o The equality part of the hypotheses always appears in the null hypothesis. o In general, a hypothesis test about the value of a population proportion pmust take one of the following three forms (where p is 0 the hypothesized value of the population proportion).

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