1. “What is the life expectancy for Caucasian males that have survived 54 years?” The answer will almost certainly be larger than 72. I want an estimate “conditioned on” the fact that I have already lived 54 years. Life is dynamic. Things are constantly changing. However, too often decisions are based on static information. Bayes theorem takes advantage of dynamic information to give a better, more correct answer. Bayes Theorem is a mathematical representation that helps one to calculate conditional probability. It relates inverse representation of the probabilities concerning two events. This theorem is named after the British Mathematician Thomas Bayes. It is represented by

P(A, B)= P(A B) P(B) or P (A, B)=P(B A)P(A)
So
P(A|B)P(B) = P(B|A)P(A)
The Law of Total Probability:
P(B) = P(B/A).P(A) + P(B/A′) . P(A′)
Total probability and multiplication rule:
P(A/B) = P(B/A).P(A) (multiplication rule) P(B/A).P(A) + P(B/A′) . P(A′)(Law of Total Prob.) Where:
P(A): probability of occurrence of event A (marginal)
P(B): probability of occurrence of event B (marginal)
P(A′) = probability that A does not occur
P(B/A′) = probability that event B occurs given that A has not occurred already. P(A,B): Probability of simultaneous occurrence of events A and B (joint) P(A|B): Probability of occurrence of A given that B has occurred (conditional) P(B|A): Probability of occurrence of B given that A has occurred (conditional).

2. A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.

For any continuous random variable with probability density function f(x), we have that:

...MM207 Statistics
Unit IV Mid Term Project
1. In the following situation identify the implied population.
A recent report on the weekly news presented the findings of a study on the effectiveness of Onglyza, along with diet and exercise, for treating diabetes.
According to Bennett (2009), a population is defined as “the complete set of people or things being studied” in a statistical study. Given that the information is in relation to finding the success of a drug used to care for diabetes, the population would be individuals who experience diabetes. Therefore, the implied population is the entire individual’s who diabetics are. Individuals who are diabetics are those who were used to test the effectiveness of Onglyza, diet and exercise.
2. In the following scenario identify the type of statistical study that was conducted.
A Gallop poll surveyed 1,018 adults by telephone, and 22% of them reported that they smoked cigarettes within the past week.
I would say that this would be an observational study which is a study when specific characteristics of the subject are observed, but the characteristics are in no way customized by the researcher. The reason I say that this would be an observational study is because the sample population that was studied was not influenced by the researcher themselves. In addition based on the fact that this study was a poll, in which people were asked to answer the questions but no responses were...

...Review Sheet for Exam #2
As was the case in your first exam, an important aspect of your learning in this course is what you will know about the terms and concepts that are used in Applied Statistics. You can consider the terms the language of the discipline. It increases the credibility of your work for you to have a good grasp of this language. With this in mind, I will evaluate what you know about the following terms/concepts/ideas. I suggest you learn what they are from reading your slides and your text if you are uncertain about their meanings and how they are applied. Your quiz will be made up of multiple–choice questions.
1. Normal distribution and its properties, such as the shape of the bell-curve and why
2. Example of events that follow Binomial Distributions
3. Properties of Binomial Distribution – mean, variance and standard deviation
4. Probability density function and areas under the distribution curve
5. Standard deviation and the shape of a bell curve
6. Why standardize random variables
7. Mean and Standard deviation of a Binomial distribution
8. What Estimation is, as the concept relates to sampling theory
9. What the Central Limit Theorem is
10. Point estimates – what these are? For example, the sample mean as an estimate of the population mean or sample proportion as an estimate of population proportion
11. Finite population correction factor
12. Standard Error of estimates – s/ and σ/
13. Calculating margin of error associated with...

...STATISTICS - Lab #6
Statistical Concepts:
Data Simulation
Discrete Probability Distribution
Confidence Intervals
Calculations for a set of variables
Open the class survey results that were entered into the MINITAB worksheet.
We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select the mean column. Click OK and the mean for each observation will show up in the Worksheet.
We also want to calculate the median for the 10 rolls of the die. Label the next column in the Worksheet with the word median. Repeat the above steps but select the radio-button that corresponds to Median and in the Store results in: text area, place the median column.
Calculating Descriptive Statistics
Calculate descriptive statistics for the mean and median columns that where created above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to mean and median. The output will show up in your Session Window. Print this information.
Calculating Confidence Intervals for one Variable
Open the class survey results that were entered into the MINITAB worksheet.
We are interested in...

...Statistics – Lab #6
Statistical Concepts:
* Data Simulation
* Discrete Probability Distribution
* Confidence Intervals
Calculations for a set of variables
Mean Median
3.2 3.5
4.5 5.0
3.7 4.0
3.7 3.0
3.1 3.5
3.6 3.5
3.1 3.0
3.6 3.0
3.8 4.0
2.6 2.0
4.3 4.0
3.5 3.5
3.3 3.5
4.1 4.5
4.2 5.0
2.9 2.5
3.5 4.0
3.7 3.5
3.5 3.0
3.3 4.0
Calculating Descriptive Statistics
Descriptive Statistics: Mean, Median
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
Mean 20 0 3.560 0.106 0.476 2.600 3.225 3.550 3.775 4.500
Median 20 0 3.600 0.169 0.754 2.000 3.000 3.500 4.000 5.000
Calculating Confidence Intervals for one Variable
One-Sample T: Sleep
Variable N Mean StDev SE Mean 95% CI
Sleep 20 6.950 1.572 0.352 (6.214, 7.686)
One-Sample T: Sleep
Variable N Mean StDev SE Mean 99% CI
Sleep 20 6.950 1.572 0.352 (5.944, 7.956)
Short Answer Writing Assignment
All answers should be complete sentences.
1. When rolling a die, is this an example of a discrete or continuous random variable? Explain your reasoning.
It is a discrete since rolling a die, we only have a 1/6 chances when rolling a number. Besides, it is always a concrete number it is never a 1.0001 chances, 1.00000001, or 1.00001, or anything between. |
2. Calculate the mean and standard...

...QNT 273 – INTRODUCTION TO BUSINESS STATISTICS – Complete Class Includes All DQs, Individual and Team Assignments – UOP Latest
Purchase this tutorial here: https://www.homework.services/shop/qnt-273-introduction-to-business-statistics-complete-class-includes-all-dqs-individual-and-team-assignments-uop-latest/
QNT 273
Introduction to Business Statistics
Week 1:
Individual Assignment: Introduction to Statistics Paper
Write a 350- to 700-word paper in which you describe how you use statistics in your everyday life.Include your definition of statistics and the relative value of statistics in your life.
Week 2:
Individual Assignment: Textbook Assignment
Complete Review Exercise 7 in Ch. 1 of Elementary Statistics.
Learning Team Assignment – Textbook Assignments
Complete Exercises 2–3: Problems 13 & 14 in Ch. 2 of Elementary Statistics.
Complete Exercise 2.4 in Ch. 2 of Introductory Statistics.
Learning Team Assignment: Misleading Graphs Paper and Presentation
Locate an example of a misleading graph such as inconsistent units, missing legends, lacking reference, or gaps in data.
Write a 350- to 700-word paper in which you describe the problems associated with the graph and how the problems might affect the users.
Describe what must be done to correct the graph.
Format your paper consistent with APA guidelines....

...Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of information, or the quantitative description itself. Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
Statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. Inferential statistics are used to test hypotheses and make estimations using sample data.
Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many sciences
Qualitative Variables or Categorical Variable
Also known as categorical variables, qualitative variables...

...
What is Bootstrapping (In Statistics)?
Bootstrapping is an interesting process or technique of assigning measure of accuracy. Depended upon calculation, Bootstrapping can be used to any statistic to measure estimation.
Definition
According to the Cambridge dictionary of statistics – “A conﬁdence interval is a range of values, calculated from the sample observations that are believed, with a particular probability, to contain the true parameter value. A 95% conﬁdence interval, for example, implies that were the estimation process repeated again and again, then 95% of the calculated intervals would be expected to contain the true parameter value.”
Reason for the name
The term has been derived from the expression "lifting oneself up by one's own bootstraps". This refers to raising oneself up by one's own means. This is also called bootstrap funding.
Example
Let’s understand this with an interested example of a candy factory. Knowing that the candy bars have mean weight. Since it is not feasible to weigh each candy that is produced in the factory, we use sampling techniques and randomly choose 100 candies. We calculate the mean of these 100 candies, and say that the population mean falls under a margin of error.
Suppose that after a couple of months, we want to know the mean candy weight on the day that we sampled the production line (with greater accuracy - or less of a margin of error).
We simply cannot use...

...2/8 (Friday)
Standard Deviation cont’d
Example: Amount of money earned by new immigrants
Sample: 12, 15, 16, 20, 25, 36, 40
Step 1: Find the mean
* x̄=164/7
* mean is 23.4
Step 2: Find how much each observation deviates from the mean
* 12 - 23.4 = -11.4
* 15 – 23.4 = -8.4
* 16 – 23.4 = -7.4
* 20 – 23.4 = -3.4
* 25 – 23.4 = 1.6
* 36 – 23.4 = 12.6
* 40 – 23.4 = 16.6
* Note: all observations below mean will be negative, all above will be positive
Step 3: Square the deviations
* (-11.4)² = 129.96
* (-8.4)² = 70.56
* (-7.4)² = 54.76
* (-3.4)² = 11.56
* (1.6)² = 2.56
* (12.6)² = 158.76
* (16.6)² = 275.56
Step 4: Add them together
* 129.96 + 70.56 + 54.76 + 11.56 + 2.56 + 158.76 + 275.56 = 703.72
Steps 5 & 6:
* Divide sum from sample size
* 703.72/7 = 100.53
* Take square root of the number
* √100.53 = 10.03 – round two places out
* This means that, on average, the income of new immigrants deviates almost $10.000 from the mean.
* This is a relatively large deviation (almost half the mean)
* There is a lot of variability in how much new immigrants earn.
The Normal Range
* Within 1 standard deviation of the mean
* Contains cases considered close to the norm
Variation
* Very similar to standard deviation
* Formula:
* To calculate variation, square the standard deviation
What do we know?
* Distributions – categorizing and graphing...