Testing statistical significance is an excellent way to identify probably relevance between a total data set mean/sigma and a smaller sample data set mean/sigma, otherwise known as a population mean/sigma and sample data set mean/sigma. This classification of testing is also very useful in proving probable relevance between data samples. Although testing statistical significance is not a 100% fool proof, if testing to the 95% probability on two data sets the statistical probability is .25% chance that the results of the two samplings was due to chance. When testing at this level of probability and with a data set size that is big enough, a level of certainty can be created to help determine if further investigation is warranted. The following is a problem is used to illustrate how testing statistical significance paints a more descriptive picture of data set relationships. Sam Sleep researcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a management ability test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SMAT (Sam's Management Ability Test) to all participants. (Scores on the SMAT range from 1-9 with high scores representing better performance). Is Sam's hypothesis supported by this data? SMAT scores

8 hours sleep group (X)57535339
4 hours sleep group (Y)81466412

When given a data set one of the most important evaluations is to determine if the data set size is big enough to show relevance. So, the first thing I did was to check if the size warranted further review. Finding the smallest relevant size of data is as simple as taking the confidence quotient and multiplying this by the standard deviation to the second power. Taking this sum and dividing by .6 of the standard deviation. Another word for standard deviation is sigma and from this point forward I will use S to represent a population’s sigma and s to represent a sample set sigma. In this situation, the first data set equation looks like:

The second data set returned 8.37 because the sigma for the second data set was bigger than the first. Both of these numbers need to be rounded up to the nearest whole number and then compared to the sample size. The first sample set is equal to the recommended smallest sample size however the second sample size falls short by one datum. This test leads me to believe that the sample sizes are not big enough to stand up to significant scrutiny. Be that as it may, the data was put into a distribution chart to compare the distribution patterns to see any significant difference however, there was no significant difference. The next step to finding if there was a change between the samplings was to test the sigmas in an f test. This test takes the larger sigma squared and divides by the smaller sigma squared to create f. Then compares the number of datum in the sample to an f chart that gives a range of numbers and if the f falls between the range specified for the number of datum in the sample then the sigmas are not significantly different. This test shows that there is not a 95% probability that the samplings are significantly different and therefore does not support Sam’s theory. Taking this to the next statistical significance test takes us to a t test. To be specific, the test used in this comparison is the t test of two sample averages. However, this equation gets a little complicated for words so, it is best to illustrate this computation. Before doing so we need to establish some symbology for each of the numbers. 1 = the mean of group X2 = the mean of group Y n1 = the number of datum in group X n2 = the number of datum in...

...Hypothesis Testing For a Population Mean
The Idea of Hypothesis Testing
Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test:
H0: = 190
H1: > 190
We test 100 only children and find that
x = 198
and suppose we know the population standard deviation
= 15.
Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have
z is called the test statistic.
Since z is so high, the probability that Ho is true is so small that we decide to reject H0 and accept H1. Therefore, we can conclude that only children have a higher average cholesterol level than the national average.
Rejection Regions
Suppose that = .05. We can draw the appropriate picture and find the z score for -.025 and .025. We call the outside regions the rejection regions.
We call the blue areas the rejection region since if the value of z falls in these regions, we can say that the null hypothesis is very unlikely so we can reject the null hypothesis
Example
50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.7 hours of sleep. We follow...

...Simple Hypothesis: A statistical hypothesis which specifies the population completely (i.e. the form of probability distribution and all parameters are known) is called a simple hypothesis.
1. Composite Hypothesis: A statistical hypothesis which does not specify the population completely (i.e. either the form of probability distribution or some parameters remain unknown) is called a Composite Hypothesis.
Hypothesis Testing or Test of Hypothesis or Test of Significance
Hypothesis Testing is a process of making a decision on whether to accept or reject an assumption about the population parameter on the basis of sample information at a given level of significance.
Null Hypothesis: Null hypothesis is the assumption which we wish to test and whose validity is tested for possible rejection on the basis of sample information.
It asserts that there is no significant difference between the sample statistic (e.g. Mean, Standard Deviation(S), and Proportion of sample (p)) and population parameter (e.g. Mean(µ), standard deviation (σ), Proportion of Population (P)).
Symbol-It is denoted by Ho
Acceptance- The acceptance of null hypothesis implies that we have no evidence to believe otherwise and indicates that the difference is not significant.
Rejection- The rejection of null hypothesis implies that it is false and indicates that the difference is significant....

...with an attached garage ranges from (57-82) and we are 95% confident about it.
4. Refer to the Real Estate data, which report information on the homes sold in Denver, Colorado, last year. [Chapter-10]
I. A recent article in the Denver Post indicated that the mean selling price of the homes in the area is more than $2200. Can we conclude that the mean selling price in the Denver area is more than $2200? Use the .01 significance level. What is the p-value?
II. The same article reported the mean size was more than 2100 square feet. Can we conclude that the mean size of homes sold in the Denver area is more than 2100 square feet? Use the .01 significance level. What is the p-value?
Answer to the question No.4
i. Hypothesis testing:
Step1: State the Null Hypothesis (H0) and Alternative Hypothesis (H1)
H0 : μ ≤ $ 2200 i.e.; mean selling price of homes in Denver is not more than $2200
H1 : μ > $ 2200 i.e.; mean selling price of homes in Denver is more than $2200
Step 2: select the level of significance
Here, the level of significance is, α = .01
Step 3: Determine the appropriate test statistic
t-test statistic will be used here.
Step 4: Formulate the decision rule
If p-value < α – value (or calculated value is greater than critical value), H0 is rejected
If p-value > α- value (or calculated value is less than critical value), H0 is accepted
Step 5: Select the...

...report aims to analyse and interpret the data set of 200 records regarding the CCResort. The given information includes booking identification number, income, number of people per booking, length of stay, age and overall expenditure.
From the booking ID it can be assumed that the selection of data is random, however as it is only partial information and not the population, the period of time in which the data is selected from would affect the end results of analysis.
The report is divided into two sections outlining the statistical analysis of data and hypothesis testing to observe if CCResort have met their 2 major key performance indicators (KPIs)
1 More than 40% of their customers stay for a full week (i.e. seven nights);
2 The average customer spends more than $255 per day in excess of accommodation costs.
Figures at a glance
This section of the report aims to give users a better understanding of the data through statistical data analysis of investigation categories including family income, expenditure habits, age distribution, the number of people per booking and their length of stay. These analysis are meaningful in giving users a better understanding of the customer base in relation to the key performance indicators.
1. Family income distribution
From the data collected, 62 families (31% of the sample) earn an income of more than $100,000 while 69% of the sample (138 bookings) had...

...Dependent = Score on test
b) Assuming a two-tailed test, state null hypothesis that includes the independent & dependent variable.
Ho: After the program the mean will still be 150
H1: After the program the mean will be different from 150
c) Using symbols, state the hypotheses (H and H) for the two tailed test.
Ho: u=150
H1: μ ≠150
d) Sketch the appropriate distribution, and locate the critical region for u=.05
Put 150 instead of 50 for u
e) Calculate the test statistic (z-score) for the sample
qm = q / square root of number in sanple = 25 / sq root of 25 = 25 / 5 = 5
Z= M - u / qm = 158 - 150 / 5 = 8 / 5 = 1.6
f) what decision should be made about the null hypothesis, & the effects of the program?
- a statistical decision about the Null hypothesis.
- and a conclusion about the outcome of the experiment.
10) State college is evaluating a new English composition course for freshman.
A random sample of n=25 freshman is obtained and the students are placed
in the course during their first semester. One year later, a writing sample is obtained
for student and the writing samples are graded using a standardized evaluation
technique. The average score for the sample is M=76. For the general population
of college students, writing scores from a normal distribution with a mean of u=70.
a) If the writing scores for the population have a standard deviation of q=20, does the sample
provide enough evidence to...

...Hypothesis Testing
Index:
1. What is Hypothesis testing in Business Intelligence terms?
2. Define - “Statistical Hypothesis Testing” – “Inferences in Business” – and “Predictive Analysis”
3. Importance of Hypothesis Testing in Business with Examples
4. Statistical Methods to perform Hypothesis Testing in Business Intelligence
5. Identify Statistical variables required to compute Hypothesis testing.
a. Correlate computing those variables from the data available in normalized tables arranged in row x columns.
6. Computing Statistical Hypothesis Testing for Business Decisions using Algorithms
7. User Interface Development for Presentation of Hypothesis feature
8. How does it fit in Prajna?
1. What is Hypothesis testing in Business Intelligence?
Hypothesis Testing – 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 look at the values of the index with the percentage increase or decrease in rainfall during the year compared to previous years.
Hypothesis Testing is a study...

...will
briefly discuss those elementary statistical concepts that provide the necessary
foundations for more specialized expertise in any area of statistical data analysis. The
selected topics illustrate the basic assumptions of most statistical methods and/or have
been demonstrated in research to be necessary components of one's general
understanding of the "quantitative nature" of reality (Nisbett, et al., 1987). Because of
space limitations, we will focus mostly on the functional aspects of the concepts
discussed and the presentation will be very short. Further information on each of those
concepts can be found in the Introductory Overview and Examples sections of this
manual and in statistical textbooks. Recommended introductory textbooks are:
Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of
elementary theory and assumptions of statistics, see the classic books by Hays (1988),
and Kendall and Stuart (1979).
• What are variables?
• Correlational vs.
experimental research
• Dependent vs. independent
variables
• Measurement scales
• Relations between variables
• Why relations between
variables are important
• Two basic features of every
relation between variables
• What is "statisticalsignificance" (p-value)
• How to determine that a
result is "really" significant
• Statisticalsignificance and
the...

...CHAPTER 4 – THE BASIS OF STATISTICALTESTING
* samples and populations
* population – everyone in a specified target group rather than a specific region
* sample – a selection of individuals from the population
* sampling
* simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research
* extremely difficult, time-consuming, expensive
* cluster sampling – identify clustering units in the population
* opportunity sampling – selecting participants who just happen to be available at the time and the place that you are conducting your research
* snowball sampling – referrals from participants
* volunteer sampling – where you might advertise your study and wait for people who have read your ad to come forward to take part
* how generalizable are data?
* Q: are the means for our sample approximately equal to the mean from the population?
* randomly selected sample because of this random factor, sample may not be exactly representative
* sampling error
* the difference between the sample mean and the population mean
* ensure that you have enough participants so that you get an accurate reflection of the population that you are interested in
* population mean (parameter), sample mean (statistic)
* the larger the...