Statistical Inference - Hypothesis Testing

STATISTICAL INFERENCE -HYPOTHESIS TESTING

INTRODUCTION

Basic terminologies:

• Null hypothesis:        A claim about a population parameter which is to be tested.
• Alternative hypothesis: A claim about the population parameter if the null hypothesis is rejected.
• Type I error: An error that occurs when a true null hypothesis is rejected.
• Type II error:         An error that occurs when a false null hypothesis is not rejected.
• Test statistic: A quantity calculated from the sample information used as a basis for deciding whether or not to reject the null hypothesis.
• Decision rule: A statement of the condition or conditions under which the null hypothesis is rejected.
• Errors in hypothesis testing (Summary)

Hypothesis testing involves the following steps:

1. State the null hypothesis: Along with the null hypothesis, make a second statement called the alternative hypothesis. Accept the alternative hypothesis if you reject the null hypothesis
2. Choose a level of significance. The level of significance refers to the probability of making Type I error
3. Choose a test statistic. A test statistic is a quantity calculated from the sample information. Its value will be used in step 4 and 5 to arrive at a decision regarding the null hypothesis.
4. Set up a decision rule based on the level of significance chosen in step 2 and the sampling distribution of the test statistic ( from step 3)
5. Select one or more samples. Then, using the sample results, compute the value of the test statistic.

In this course we shall discuss two types of tests, namely

A). Tests for population means: This is divided into

1. Test of hypothesis for a single population parameter:

We apply the test statistic given by

[pic 1]

Where         [pic 2]         is the sample mean

[pic 3]         is the population mean

[pic 4]         is the standard error of the mean, [pic 5]is the population  standard deviation. If  [pic 6] is unknown, we use sample standard deviation, s