1. How large a sample was needed for the Voss et al. (2004) study according to the power analysis? Was this the minimum sample size needed for the study or did the researchers allow for sample mortality?

Answer: After conducting a power analysis, the researchers planned a sample size of 96 patients for their study. The 96 subjects allowed for 30 subjects per group for the three study groups plus 6 subjects for sample mortality or attrition.

2. What was the sample size for the Voss et al. (2004) study? Was this sample size adequate for this study? Provide a rationale for your answer.

Answer: The sample size for this study was N = 62. The power analysis indicated that a sample of 96 was needed and the 62 subjects in the sample were less than was projected by the power analysis. However, preliminary analyses after the 62 patients were enrolled revealed significant groups differences. Since significant group differences were found, then the sample size was adequate and no Type II error occurred of saying the groups were not significantly different when they were.

3. What effect size was used in conducting the power analysis for this study? What effect size was found during data analysis and how did this effect the sample size needed for this study?

Answer: A moderate effect size of 0.33 was used to conduct the power analysis. During data analysis, the researchers indicated that significant group differences and large effect sizes were found for anxiety, pain sensation, and pain distress. Since a large effect size was found during data analysis, the sample size of 62 was adequate to detect significant group differences versus the 96 projected in the power analysis. The larger the effect size, the smaller the sample needed to detect group differences.

4. What power was used to conduct the power analysis in the Voss et al. (2004) study? What amount of error exists with this power level? Provide a rationale for your answer....

...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 hypothesis testing, 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, etc.) described in the analysis plan.
Interpret results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis.
Decision Errors
Two types of errors can result from a hypothesis test.
Type I error. A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level. This probability is also called alpha, and is often denoted by α.
Type II error. A Type II error occurs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often...

...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. 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 about
* How to test a sample against a benchmark?
* How to assess the risk of incorrect decisions?
Identifying the confidence...

...In today’s world, we are faced with situations everyday where Statistics can be applied. In general, Statistics is the science of collecting, organizing, and analyzing numerical data. The techniques involved in Statistics are important for the work of many professions, thus the proper preparation and theoretical background of Statistics is valuable for many successful career paths. Marketing campaigns, the realm of gambling, professional sports, the world of business and economics, the political domain, education, and forecasting future occurrences are all areas which fundamentally rely on the use of Statistics. Statistics is a broad subject that branches off into several categories. In particular, Inferential Statistics contains two central topics: estimation theory and hypothesis testing.
The goal of estimation theory is to arrive at an estimator of a parameter that can be implemented into one’s research. In order to achieve this estimator, statisticians must first determine a model that incorporates the process being studied. Once the model is determined, statisticians must find any limitations placed upon an estimator. These limitations can be found through the Cramer-Rao lower bound. Under smoothness conditions, the Cramer-Rao lower bound gives a formula for the lower bound on the variance of an unbiased estimator. Once the estimator is developed, it is tested...

...MBA SEMESTER 1
MB0040 – STATISTICS FOR MANAGEMENT
Assignment
Roll No.
1- Statistical survey is a scientific process of collection and analysis of numerical data used to collect information about units.
Questionnair and schedule are both methods of collecting data in statistical survey. At questionnair the questions is sent by mail to respondents to fill it and send it back. At schedule the questions is filled by the enumerator.
Questionnair is a cheaper process than schedule when it was in a large samples or population. Questionnair should be filled by litrate and cooperative but scheduke is filled enumurator. Risk of misunderstanding of quwstions in questionnair is more than schedule.
2- Data representation of family expenditure using Pie Chart
3-
X = X1*n1 + X2*n2
n1 +n2
where X = Combined arithmetic mean = 10.9
X1 = arithmetic mean of sample (1) = 10.4 and n1 = No. of sample (1) = 100
X2 = arithmetic mean of sample (1) = ? and n1 = No. of sample (2) = 150
So… 10.9 = 10.4 * 100 + X2 * 150
100 + 150
2725 = 1040 + X2 * 150 1685 = X2 * 150
X2 = 11.23
So the average weight of screws of box B = 11.23
4- (a) As a decision maker in many cases you have to take action about implementing, producing or manufacturing either of one or two or some times more course of actions. With the help of rules of probability...

...2a) 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.
4a) The boundaries for critical region, when alpha level is is changed from α = .05 to .01, the size of the critical region will increase in size and the boundaries will be closer to the center of the distribution. This will allow me to see if there is error or not and also accept or reject the null hypothesis. 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.
4b) The probability of a Type I error is determined by the alpha level. Since the alpha level has decreased, we can expect increase in error.
6a) The independent variable is the application of study –skills training...

...positive slope. / R=-1 fall along a straight line with a negative slope. \ R=0 no linear relationship between variables. --- Limits on correlation coefficients- can only use if both are interval, and sensitive to outliers, does not capture non-linear relationships, does not show the strength of relationships. Interquartile range- location measure, shows outliers. Regression- how close the value is to the line (r^2) y=a+bx a= intercept. B= slope. Intercept is y=? when x=0. Regression line explains the variation of the dependant variable, the higher the # the more accurate the regression. Regression Formula Y=a+b*x. Regression is the value that makes the sum of all y hat- y mean squared the smallest possible. Coeffectient: when reading regression coefficient chart use “unstandardized” column and when independent goes up one dependent goes up by XXX. Intercept: value of y when x=0, Intercept is first # under B, coefficient is second # under b. Standard error of estimate: how to calculate the average deviation of a regression line: s= square root of (1/n-2)* ∑ i(Yi-p)^2. z-score= data value- mean/stand.dev. Experimental design: control group with random assignment. Quasi-experimental design: either control group or random assignment. Non-experimental design: no control group no random assignment Conceptual def.: what one thinks of or means related to an abstract idea . Operational def.: specific definition based on conceptual...

...Section 1: Review and Preview
* Chapters 2 and 3 used “descriptive statistics when summarizing data using tools (such as graphs), and statistics (such as mean and standard deviation)
* Methods of inferential statistics use sample data to make an inference or conclusion about a population
* Two main activities of inferential statistics are using sample data to…
* Estimate a population parameters
* Such as estimating a population parameter with a confidence interval
* Test a hypothesis or claim about a population parameter
* Chapter 7 presented methods for estimating a population parameter with a confidence intervals
* This chapter presents the method of hypothesis testing
* A hypothesis is a claim or statement about a property of a population
* A hypothesis test (or test of significance) is a procedure for testing a claim about a property of a population
* Main objective of this chapter is to develop the ability to conduct hypothesis tests for claim made about a population proportion “p”, a population mean “μ”, or a population standard deviation “σ”
* Formal method of hypothesis testing uses several standard terms and conditions in a systemic procedure
* CAUTION: When conducting hypothesis tests instead of jumping directly to procedures and calculations, be sure to consider context of data, source of data, and sampling method used to obtain...

...Key Synthesis/Potential Test Questions (PTQs)
• What is statistics? Making an inference about a population from a
sample.
• What is the logic that allows you to be 95% confident that the confidence interval contains the population parameter?
We know from the CLT that sample means are normally distributed around the real population mean (). Any time you have a sample mean within E (margin of error) of then the confidence interval will contain . Since 95% of the sample means are within E of then 95% of the confidence interval constructed in this way will contain.
• Why do we use confidence intervals verses point estimates? The sample mean is a point estimate (single number estimate) of the population mean – Due to sampling error, we know this is off. Instead, we construct an interval estimate, which takes into account the standard deviation, and sample size.
– Usually stated as (point estimate) ± (margin of error)
• What is meant by a 95% confidence interval? That we are 95% confident that our calculated confidence interval actually contains the true mean.
• What is the logic of a hypothesis test?
“If our sample result is very unlikely under the assumption of the null hypothesis, then the null hypothesis assumption is probably false. Thus, we reject the null hypothesis and infer the alternative hypothesis.”
• What is the logic of using a CI to do a HT?
We are 95% confident the proportion is in this interval… if the sample mean or...