Previously a group of friends compared the average temperature for the 15 days in each of the 2004 and 2005 Christmas holiday pubic school vacations to determine which holiday was colder. Secondary research retrieved from the National Oceanic and Atmospheric Administration's (NOAA) National Weather Service website provided climatic data on a daily basis for each day of the periods under investigation. Daily average temperature for each of the 15-day holiday vacation periods were gathered as two samples. The friends established a null hypothesis that the Christmas holiday vacation period of 2004 was colder than that of the 2005 Christmas holiday vacation period. After the completion of a five-step hypothesis test using a t-test, the null hypothesis was accepted. The acceptance of this null hypothesis led to further discussion on the comparison of the two periods. The suggestion arose that perhaps the 2004 holiday vacation was colder in part due a higher occurrence of weather changes. The friends agreed that the arrival of colder winter weather always seemed to follow a period of increased winds. A new hypothesis that the colder 2004 Christmas vacation period was windier than that of 2005 was developed. The friends researched the wind speed of the holiday periods and implemented the five-step process for hypothesis testing. Hypothesis

The average wind for the 15 days in 2004 Christmas holiday vacation is not equal to the average wind speed for 15 days of the 2005 Christmas holiday vacation.

After secondary research from the National Weather Service (2006), the mean wind speed for the 2004 Christmas holiday vacation is calculated at approximately 6.6 mph and serves as the population mean wind speed in the test statistic.

The null and alternate hypotheses are stated:
H0: H1:
The result of this hypotheses test will allow the friends to determine if the...

...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...

...Statistics for Business Intelligence – HypothesisTesting
Index:
1. What is Hypothesistesting in Business Intelligence terms?
2. Define - “Statistical HypothesisTesting” – “Inferences in Business” – and “Predictive Analysis”
3. Importance of HypothesisTesting in Business with Examples
4. Statistical Methods to perform HypothesisTesting in Business Intelligence
5. Identify Statistical variables required to compute Hypothesistesting.
a. Correlate computing those variables from the data available in normalized tables arranged in row x columns.
6. Computing Statistical HypothesisTesting for Business Decisions using Algorithms
7. User Interface Development for Presentation of Hypothesis feature
8. How does it fit in Prajna?
1. What is Hypothesistesting in Business Intelligence?
HypothesisTesting – is used to prove or disprove the research (Business proposed decision) hypothesis by providing more measurable or concrete hypothesis statement. for example, a research hypothesis could be that the stock market index reflects the state of monsoon in the country. A statistical hypothesis might...

...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...

...What is HypothesisTesting?
A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesistesting refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.
Statistical Hypotheses
Null hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance.
Alternative hypothesis. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause.
Hypothesis Tests
Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesistesting, consists of four steps.
State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.
Formulate an analysis plan. The analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic.
Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score,...

...
a. Testing a Hypothesis: In Unit 5 you began to study the use of hypothesistesting to answer research questions. Rewrite your research question, null hypothesis, and alternative hypothesis from Unit 5 here. Make any needed improvements to create an appropriate hypothesis test that can be tested using the t or z test statistic to compare means.
Write yourhypothesis here. My hypothesis is whether there is a difference in the mean scores on the MCAT for men and women.
Write your null hypothesis here.
H0: Men MCAT score = Women MCAT score
Write your research (alternative) hypothesis here
Ha: Men MCAT score ≠ Women MCAT score
What two means are you comparing? The two means I would be comparing are the mean MCAT score for men vs. the mean MCAT score for women.
Is your test one-tailed or two-tailed? My test is a two-tailed test because the alternative hypothesis is looking at where the MCAT score for men and women are not equal.
b. Samples and Populations: Given your research question and hypothesis above, what would your population of interest be?
Describe your population.
My population of interest is: men and women between the ages of 22 and 30 that have taken the MCAT one time.
Describe the population – what does it contain? The population contains...

...HypothesisTesting 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...

...to
HypothesisTesting
8.1
Inferential Statistics
and HypothesisTesting
LEARNING OBJECTIVES
8.2 Four Steps to
HypothesisTesting
After reading this chapter, you should be able to:
8.3
HypothesisTesting and
Sampling Distributions
8.4
Making a Decision:
Types of Error
8.5
Testing a ResearchHypothesis: Examples
Using the z Test
8.6
Research in Focus:
Directional Versus
Nondirectional Tests
8.7
Measuring the Size of
an Effect: Cohen’s d
8.8
Effect Size, Power, and
Sample Size
8.9
Additional Factors That
Increase Power
1 Identify the four steps of hypothesistesting.
2 Define null hypothesis, alternative hypothesis,
level of significance, test statistic, p value, and
statistical significance.
3 Define Type I error and Type II error, and identify the
type of error that researchers control.
4 Calculate the one-independent sample z test and
interpret the results.
5 Distinguish between a one-tailed and two-tailed test,
and explain why a Type III error is possible only with
one-tailed tests.
6 Explain what effect size measures and compute a
Cohen’s d for the one-independent sample z test.
7 Define power and identify six factors that influence power....

...HYPOTHESISTESTING
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 hypothesistesting
• It is represented in a % age...