TESTING OF HYPOTHESIS
DEFINITIONS:
Population: It is the set or collection of objects, actual or hypothetical under study. Mainly
population consists of sets of numbers, measurements or observations which are of interest.
Size: The size of the population ‘n’ is the number of objects or observations in the
population.
Sampling: This is the process of drawing samples from a given population.
Statistic: Any function of the random variables constituting a random sample is called a
statistic.
Large Sampling: If n > 30, the sampling is said to be large sampling, otherwise it is small
sampling.
Statistical Inference: This deals with the methods of drawing valid or logical generalizations
and predictions about the population using the information contained in the sample alone.
Testing of Hypothesis:
A statistical hypothesis, or just hypothesis, is a claim or assertion either about the value of a
single parameter (population characteristic or characteristic of a probability distribution),
about the values of several parameters, or about the form of an entire probability distribution.
One example of a hypothesis is the claim, where m is the true average inside diameter of a
certain type of PVC pipe. Another example is the statement, where p is the proportion of
defective circuit boards among all circuit boards produced by a certain manufacturer. If m1
and m2 denote the true average breaking strengths of two different types of twine, one
hypothesis is the assertion that, and another is the statement. Yet another example of a
hypothesis is the assertion that the stopping distance under particular conditions has a normal
distribution. The process of deciding whether to accept or reject the the hypothesis is called
the testing of hypothesis.
Null Hypothesis: The null hypothesis formulated for the sake of rejecting it under the
assumptions is true, is called null hypothesis. and is denoted by H0.
Alternative Hypothesis: The opposite of null hypothesis is called alternative hypothesis, and
is denoted by H1.
Level of significance: The probability level below which we reject the hypothesis is called
level of significance.
Test statistic: It is a function of the sample data on which the decision (reject H 0 or do not
reject H0) is to be based
2. A rejection region, the set of all test statistic values for which H0 will be rejected
TESTING OF HYPOTHESES - LARGE SAMPLE - SINGLE MEAN
Critical Region
Steps in Testing of Hypothesis
1. Identify the parameter of interest and describe it in the context of the problem situation.
2. Determine the null value and state the null hypothesis.
3. State the appropriate alternative hypothesis.
4. Give the formula for the computed value of the test statistic (substituting the null value and
the known values of any other parameters, but not those of any samplebased quantities).
5. State the rejection region for the selected significance level a.
6. Compute any necessary sample quantities, substitute into the formula for the test statistic
value, and compute that value.
7. Decide whether H0 should be rejected, and state this conclusion in the problem context.
Two Types of Errors
Decision Table
Null Hypothesis
True
Type I Error
Correct Decision
Decision
Reject H0
Accept H0
False.
Correct Decision
Type II Error
Definition: A Type I error for a statistical test occurs if you reject the null hypothesis when
it is true. The probability of making Type I error is denoted by α.
A Type II error for a statistical test occurs if you accept the null hypothesis when it is false.
The probability of making Type II error is denoted by β.
TEST OF HYPOTHESIS FOR LARGE SAMPLES
Critical value Table for Z Test
Test
Zα
Two tail
One tail
1%
2.575
2.33
Level of significance (α)
2%
5%
2.33
1.96
2.575
1.645
10%
1.645
1.96