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...

...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...

...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)...

...(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...

...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...

...Statistics for Business Intelligence – 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....

...Elementary Concepts in Statistics
Overview of Elementary Concepts in Statistics. In this introduction, we 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...

...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...