A hypothesis is a claim
Population mean
The mean monthly cell phone bill in this city is μ = $42
Population proportion
Example: The proportion of adults in this city with cell phones is π = 0.68 States the claim or assertion to be tested
Is always about a population parameter, not about a sample statistic

Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove

Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove

Is the opposite of the null hypothesis
e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo
Alternative never contains the “=”sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove

If the sample mean is close to the stated population mean, the null hypothesis is not rejected.

If the sample mean is far from the stated population mean, the null hypothesis is rejected.

How far is “far enough” to reject H0?

The critical value of a test statistic creates a “line in the sand” for decision making -- it answers the question of how far is far enough.

Type I Error
Reject a true null hypothesis
Considered a serious type of error
The probability of a Type I Error is
Called level of significance of the test
Set by researcher in advance
Type II Error
Failure to reject a false null hypothesis
The probability of a Type II Error is β

Type I and Type II errors cannot happen at
the same time
A Type I error can only occur if H0 is true
A Type II error can only...

...Chapter-11
Testing of Hypothesis:
(Non-parametric Tests)
Chapter-11: Testing of Hypothesis - (Non-parametric Tests)
2
11.1. Chi - square ( χ )Test / Distribution
2
11.1.1. Meaning of Chi - square ( χ )Test
2
11.1.2. Characteristics of Chi - square ( χ )Test
2
11.2. Types of Chi - square ( χ )Test / Distribution
2
11.2.1. Chi - square ( χ )Test for Population Variance
2
11.2.2. Chi - square ( χ )Test for Goodness-of-Fit
2
11.2.3. Chi - square ( χ )Test or Independence
11.3. Analysis of Variance (ANOVA)
11.3.1. Meaning of ANOVA
11.3.2. ANOVA Approach
11.4. ANOVA Technique
11.4.1. One-way ANOVA
11.4.2. Two-way ANOVA
11.4.3. ANOVA in Latin-square Design
11.5. Other Nonparametric Techniques
Summary:
Key Terms:
Questions:
11.1. CHI-SQUARE (
) TEST /DISTRIBUTION
2
11.1.1. Meaning of Chi - square ( χ )Test
2
A chi-square test (also chi squared test or χ test) is any statistical hypothesis test in which the
sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true,
or any in which this is asymptotically true, meaning that the sampling distribution (if the null
hypothesis is true) can be made to approximate a chi-square distribution as closely as desired by
making the sample size large enough. The Chi-Square (
) test is the most popular non-parametric
test/methods, to test the hypothesis. The...

...
The word ‘Hypothesis is derived from a Greek word, which means ‘to suppose’. It is usually considered as the principal instrument in research. For a researcher it is a formal question that he or she intends to resolve. In this way a hypothesis may be defined as a proposition or a supposition. The main function of hypothesis is to guide the collection and processing of materials and direct the research. Hypothesis is a tentative conclusion. It is facts based theory. A research scholar will analyze the information from variety of sources in order to create a hypothesis. Hypothesis can be of two types –
- Explanatory
- Descriptive
In explanatory hypothesis researcher tries to account for a given fact and the explanation is provisional because it is based on inconclusive proof. This method is especially used in finding out laws in history. The defeat of the army of Siraj in the battle of Plassey is a fact. Various explanations are offered for this fact. Again the rise of Gandhi has been accounted for variously by various authors such as Shaid Amin and Judith Brown. These explanations are really the nature of hypothesis.
Descriptive hypothesis is employed for making a complex mass of facts, which are isolated from one another, a meaningful unit by describing it in a collective manner. To...

...Hypothesis Testing I
Pat Obi
What is a “Hypothesis?”
A statement or claim about the value of a
population parameter: μ, σ2, p
Pat Obi, Purdue University Calumet
2
Decision Rule
1.
x 0
Z
s
n
Compare calculated Z value to Z value from
Table (critical Z value)
Reject H0 if calculated Z value lies in the
rejection/significance region (i.e. region)
ALTERNATIVELY:
2.
Compare p-value to
Reject H0 if p-value <
Pat Obi, Purdue University Calumet
3
Two-Tail Test
Ex: H0: 0 = 50; H1: 0 ≠ 50. Test at α = 0.05
Reject H0 if calculated Z is either less than ZCV
on the left tail or greater than ZCV on the right
0
Rejection region: /2 = 0.025
Rejection region: /2 = 0.025
0
ZCV = -1.96
ZCV = 1.96
Pat Obi, Purdue University Calumet
4
One-Tail Test: Right/Upper Tail
Ex: H0: 0 ≤ 55; H1: 0 > 55. Test at α = 0.05
Reject H0 if calculated Z > Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = 1.645
Pat Obi, Purdue University Calumet
5
One-Tail Test: Left/Lower Tail
Ex: H0: 0 ≥ 12; H1: 0 < 12. Test at α = 0.05
Reject H0 if calculated Z < Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = -1.645
Pat Obi, Purdue University Calumet
6
Z Table (critical Z values)
Significance
Level
Zcv
One-Tail Test
Zcv
Two-Tail Test
0.10
1.285
1.645
0.05
1.645
1.960
0.01
2.326
2.576
Pat Obi, Purdue University Calumet
7
Rules Governing the Statement of
Hypothesis
In...

...Why We Don’t “Accept” the Null Hypothesis
by Keith M. Bower, M.S. and James A. Colton, M.S.
Reprinted with permission from the American Society for Quality
When performing statistical hypothesis tests such as a one-sample t-test or the AndersonDarling test for normality, an investigator will either reject or fail to reject the null
hypothesis, based upon sampled data. Frequently, results in Six Sigma projects contain
the verbiage “accept the null hypothesis,” which implies that the null hypothesis has been
proven true. This article discusses why such a practice is incorrect, and why this issue is
more than a matter of semantics.
Overview of Hypothesis Testing
In a statistical hypothesis test, two hypotheses are evaluated: the null (H0) and the
alternative (H1). The null hypothesis is assumed true until proven otherwise. If the
weight of evidence leads us to believe that the null hypothesis is highly unlikely (based
upon probability theory), then we have a statistical basis upon which we may reject the
null hypothesis.
A common misconception is that statistical hypothesis tests are designed to select the
more likely of two hypotheses. Rather, a test will stay with the null hypothesis until
enough evidence (data) appears to support the alternative.
The amount of evidence required to “prove”...

...all, the video did a fair job buttressing my understanding of hypothesis testing. The textbook explained the aspects and steps of hypothesis testing in a legible fashion, while the video helped demonstrate a real-life application.
I learned from the text that hypothesis testing is a “Procedure for deciding whether the outcome of a study (results from a sample) supports a particular theory or practical innovation (which is thought to apply to a population)” (Aron A., Aron, E., and Coups, 2011, p. 145). I also learned that hypothesis testing follows a set procedure that appears as follows:
Step 1) Restate the question as a research hypothesis and a null hypothesis about the populations
- Basically, a researcher constructs a hypothesis. Then he/she forms a null hypothesis that opposes the research hypothesis in
polar fashion. To help support one’s research hypothesis, one has to disprove the null hypothesis.
Step 2) Determine the characteristics of the comparison distribution
- When using two or more samples, one must gather information about the distribution of means.
Step 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
- Most researchers choose a significance level of 0.05 or 0.01.
Step 4)...

...RESEARCH METHODOLOGY
LESSON 20: PRINCIPLE OF HYPOTHESIS TESTING
So far we have talked about estimating a confidence interval along with the probability (the confidence level) that the true population statistic lies within this interval under repeated sampling. We now examine the principles of statistical inference to hypotheses testing. By the end of this chapter you should be able to
• Understand what is hypothesis testing • Examine issues relating to the determination of level of
How is this Done? If the difference between our hypothesized value and the sample value is small, then it is more likely that our hypothesized value of the mean is correct. The larger the difference the smaller the probability that the hypothesized value is correct. In practice however very rarely is the difference between the sample mean and the hypothesized population value larger enough or small enough for us to be able to accept or reject the hypothesis prima-facie. We cannot accept or reject a hypothesis about a parameter simply on intuition; instead we need to use objective criteria based on sampling theory to accept or reject the hypothesis. Hypotheses testing is the process of making inferences about a population based on a sample. The key question therefore in hypotheses testing is: how likely is it that a population such as one we have hypothesized to produce a sample such as the one we are looking at....

...APP6JMaloney problems 2. 4, 6, 10, 18, 22, 24
2 ) The value of the z score un a hypothesis test is influenced by a variety of factors.
Assuming that all the other variables are held constant, explain how the value
of Z is influenced by each of the following?
Z= M - u / SD
a) Increasing the difference between the sample mean and the original.
The z score represents the distance of each X or score from the mean.
If the distance between the sample mean and the population mean the z score will
increase.
b) Increasing the population standard deviation.
The standard deviation is the factor that is used to divide by in the equation. the bigger the SD,
then the smaller the z score.
c) Increasing the number of scores in the sample.
Should bring the samples mean closer to the population mean so z score will get smaller.
4) If the alpha level is changed from .05 to .01
a) what happens to the boundaries for the critical region?
It reduces the power of the test to prove the hypothesis.
You increase the chance of rejecting a true H
b) what happens to the probability of a type 1 error?
Type 1 error is falsely reporting a hypothesis,
Where you increase the chance that you will reject a true null hypothesis.
6) A researcher is investigating the effectiveness of a new study skills training program for elementary
school childreen. A sample of n=25 third grade children is selected to...

...HYPOTHESIS TESTING
WHAT IS THIS HYPOTHESIS????
• In simple words it means a mere assumption or supposition to be proved of disproved.
• But, for a researcher it is a formal question that he intends to resolve.
• Example: I assume that 1) under stress and anxiety a person goes into depression.
2) It leads to aggressive behaviour.
Eg. : Students who get better counselling in a university will show a greater increase in creativity than students who were not counselled.
• So, the hypothesis should be capable of being verified and tested.
CHARACTERISTICS
• Should be clear and precise – inferences not reliable
• Capable of being tested
“ A hypothesis is testable if other deductions can be made from it which, in turn can be confirmed or disproved by observation.”
• Should be limited in scope and must be specific
• Should be stated in simple terms -understandable by all concerned.
• Must explain the facts that gave rise to the need for explanation.
BASIC CONCEPTS: NULL & ALTERNATIVE HYPOTHESIS
• If we are to compare two methods A & B and both are equally good, then this assumption is termed as null hypothesis(H0)
• If it is stated that method A is better than method B-alternative hypothesis(Ha)
LEVEL OF SIGNIFICANCE
• A very important concept in the context of hypothesis testing
• It is represented in a % age (usually 5%), which should...

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