Chapter 9
Hypothesis Testing for Single Populations
The main objective of Chapter 9 is to help you to learn how to test hypothes on single populations, thereby enabling you to:
1. Understand the logic of hypothesis testing and know how to establish null and alternate hypothes.
2.Understand Type I and Type II errors and know how to solve for Type II errors.
3. Know how to implement the HTAB system to test hypothes.
4. Test hypothes about a single population mean when is known.
pole 5. Test hypothes about a single population mean when is unknown.
6. Test hypothes about a single population proportion.
7. Test hypothes about a single population variance.
CHAPTER OUTLINE
words i couldn t say1. Introduction to Hypothesis Testing
Types of Hypothes
Rearch Hypothes
Statistical Hypothes
八年级英语教案Substantive Hypothes
Using the HTAB System to Test Hypothes
Rejection and Non-rejection Regions
erasmus Type I and Type II errors
2. Testing Hypothes About a Population Mean Using the z Statistic
Using a Sample Standard Deviation
Testing the Mean with a Finite Population
Using the p-Value Method to Test Hypothes
Using the Critical Value Method to Test Hypothes
Using the Computer to Test Hypothes about a Population Mean Using
nospot the z Test
3 Testing Hypothes About a Population Mean Using the t Statistic
Using the Computer to Test Hypothes about a Population Mean Using
the t Test
4 Testing Hypothes About a Proportion
Using the Computer to Test Hypothes about a Population Proportion
Hypothesis:
Any statement about the parameters of a population is called a hypothesis. The parameters of a population are μ三年级学英语上册 , σ核销英文, p . μ means the average in the population, σ means the standard deviation in the population, and P is the population proportion. A statement about the sample characteristic is not a hypothesis.
The first step in testing a hypothesis is to establish a null hypothesis and an alternative hypothesis.
(i)Consider the following null and alternative hypothes.
Ho: μ 7 Ha: μ > 7
The hypothes are valid. This is a right tail test. The name depends on the alternative hypothesis
(i)Consider the following null and alternative hypothes.
Ho: μ 7 Ha: μ > 6
The are not valid hypothes.
(ii)Consider the following null and alternative hypothes.
Ho: 352 Ha: > 352
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The hypothes are not valid as they do not reference a population parameter.
(iii) Consider the following null and alternative hypothes.
Ho: 0.61 Ha: > 0.61
The hypothes are not valid as they do not reference a population parameter.
(iv)Consider the following null and alternative hypothes.
Ho: s 558 Ha: s < 558
The hypothes are not valid as they do not reference a population parameter.
(v)Consider the following null and alternative hypothes.
Ho: 2 35 Ha: 安徽省2012年高考分数线 2 < 35
The hypothes are valid hypothes and this is a left tail test. The name depends on the alternative hypothesis.
(vi)Consider the following null and alternative hypothes.
Ho: wujμ = 67 Ha: μ 67
The hypothes are valid hypothes. This is a two tailed hypothesis as the alternative hypothesis has a not equality sign. It means μ could be less than or more than 67. It also indicate that there is a rejection region at the left tail and another rejection region at the right tail.
(vii)Consider the following null and alternative hypothes.
Ho: P 0.16 Ha: P > 0.16
This is a right tail test of proportion with a rejection area at the right tail.
(viii)Consider the following null and alternative hypothes.
Ho: P = 0.16 Ha: P 0.16
indicate a two-tailed test with a rejection region at the left tail and another rejection region at the right tail.
Two Types of Errors
in performing a test of hypothesis
In 1982, Tylenol was considered to be dangerous a lady from California died when she took Tylenol to get rid of headache. At that time there was no protective al on the Tylenol package. It was found later that someone tampered the package and put cyanide in the Tylenol capsule. Let us consider this situation in the light of hypothesis testing to interpret the two types of error that can happen when one tests a hypothesis in real life situation.
Suppo that you are sitting in your living room and you are having headache. You just heard from the television that a lady from California died when she took Tylenol. The TV anchor is telling that you should not take Tylenol (as it could be poisonous) unless it is confirmed that there is no problem in taking Tylenol. You have a Tylenol in your hou. Should you take that Tylenol to get rid of headache? Here the null and the alternative hypothes are as follows:
