Chapters 1-3:In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157, $132, $109, $145, $125, $139. Calculate the mean and sample variance(s^2) and standard deviation. Mean = 807/6 = 134.5. Sample Variance = (109925 – (807^2/6)/6-1 = (109925 – 108541)/5 = 1384/5 = 276.8. Standard Deviation = √276.8 = 16.6373. ***the 109925 is all values of x individually squared and then summed together. ***the 6-1 is because it is a sample, if this were a population it would just be 6. ***the 807 is the sum off all x. Coefficient of Variation = (16.63/134.5)*100 = 12.3643. Calculate estimates of tolerance intervals containing 68.26, 95.44, and 99.73 percents. Mean ± 1 SD (68.26%) = 134.5 ± 16.63 = [117.87, 151.13]. Mean ± 2 SD (95.44%) = 134.5 ± 33.26 = [101.24, 167.76]. Mean ± 3 SD (99.73%) = 134.5 ± 49.89 = [84.61, 184.39]. Compute and interpret some of the Z-scores. (157-134.5)/16.63 = 1.35 standard deviations above the mean. (109-134.5)/16.63 = -1.53 standard deviations below the mean. Mean is the average of all the data. Mode is the number that occurs most frequently in the data set. Median is the middle value or average of the two middle values when the data is arranged in order from smallest to larges. Chapter 4: Basic Probability Concepts:In an organization of 30 people, we wish to elect 3 officers. How many different groups of officers are possible? 30*29*28=24,360 (if only 1 person per office). Or 30*30*30=27,000 (if 1 person can hold more than one office). Combinations: number of different combinations of N items taken n at a time: N!/n!(N-n)!. How many ways can we elect an executive committee of three from an organization of 30 members? 30!/3!(30-3)! = 24360/6 = 4060. We have four different flags and four slots on...

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D. The river/lake where a fish was captured
4. Managers study the number of days per month over the last year that employees in the payroll department called in sick to determine the averages they can expect next year. Collecting the data and determining the averages last year is an example of what type of statistics? Determining the averages they can expect next year is an example of what type of statistics?
A. They are both examples of inferential statistics because averages are inferred in both instances.
B. Inferential statistics; descriptive statistics.
C. They are both examples of descriptive statistics because they deal with analyzing data.
D. Descriptive statistics; inferential statistics.
5. The grades that a random sampling of students in the psychology degree program received over the last decade of "Abnormal Psychology" classes are an example of what statistical concept?
A. The grades are an example of a parameter.
B. The grades are an example of a sample.
C. The grades are an example of a population.
D. The grades are an example of a statistic.
6. What method is used to sample a population so that it is representative of the population?
A. All but the samples that appear to have the lowest and highest values are selected.
B. Samples are chosen at random from the...

...LEAD 6341
Research Methods and Statistics
Midterm Exam
Part I: Calculations (Open Book)
Spring, 2013
Note: For the following computational exercises, show all steps of your work (when appropriate). Do NOT simply put an answer. Show or explain how you arrived at your answer.
1) Compute the mean, median, and mode for the following distribution: (5 pts)
1,2,2,3,3,3,3,3,3,4,4,5,6,7,7,8,8,8,8,8,8,9,9,10
The mean is what people call the average. (1+2+2+3+3+3+3+3+3+4+4+5+6+7+7+8+8+8+8+8+8+9+9+10 = 127/24 = 5.2916
Mean = 5.29
The median is the middle value. When the middle does not fall neatly in the distribution, use the following formula to identify the position. In the formula n is the sample size.
Median position = (n + 1) / 2
Median position = (24 + 1)/2
Median position = 25/2 = 12.5
Now we look for position 12 and 13. Position 12 is 5, and position 13 is 6. We take the average of the two values and that is the median. Median = (5 + 6)/2 = 11/2 = 5.5
Median = 5.5
The mode is the most frequent response in the distribution
1 – 1 6 – 1
2 – 2 7 – 2
3 – 6 8 – 6
4 – 2 9 – 2
5 – 1 10 – 1
In this example we have two modes. They are 3 and 8.
2) You have been asked to give a student two different tests; an intelligence test and a creativity test. The student scored 123 on the intelligence test and 123 on the creativity test. The mean for the intelligence test is 100, and the standard...

...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...

...G036
* Yes because the p-value is less than 0.05 or No, because the p-value is greater than 0.05
* The coefficient of variation is the standard deviation of a data set, divided by the mean of the same data set.
* Z score = x -ms
* The Independent part is what you, the experimenter, changes or enacts in order to do your experiment. The dependent variable is what changes when the independent variable changes - the dependent variable depends on the outcome of the independent variable.
* P=000=P<0.001
* Repeated measure = A repeated measures design is a longitudinal study, usually a controlled experiment but sometimes an observational study
* We can be 95% confident that on average shoppers at CyberChic are between 3.37 years younger than customers at Modern Miss and 0.75 years older.
* Value of r Strength of relationship -1.0 to –0.5 or 1.0 to 0.5 Strong -0.5 to –0.3 or 0.3 to 0.5 Moderate -0.3 to –0.1 or 0.1 to 0.3 Weak –0.1 to 0.1 None or very weak
One sample t-test
A study was conducted to investigate whether the hours of work has changed for Australian men since 2001.
In a sample of 116 Australian male adults, on average the men worked 39.6 hours per week (s = 4.5). This is higher than the mean of 38.6 hours per week recorded for Australian men in 2001 and a t-test shows that the difference is significant, t (115) = 2.45, p = 0.016. The 95% confidence interval indicates that since 2001 the average hours of work has increased...

...Curve
The Bell Shaped Curve
Mean=Median=Mode
Symmetrical
Asymmetric Curve
Statistical Inference
The Central Limits Theorem: When samples are large (above 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population
Ultimate Goal
Accepting or Rejecting the NULL hypothesis
Accept or Reject?
We accept a null hypothesis when the significance level greater than .05
Reject when less than .05
Confidence Intervals
First you have to know three things:
Statistical inference: the process of using sample statistics to estimate population parameters.
Confidence level: the probability that a population parameter lies within a given confidence interval
Confidence interval: the range of values in which the population parameter is estimated to fall.
A statistic is an estimate of a parameter
But the statistic will rarely equal the parameter exactly.
Because of sample error
If our mean is 64, with a SD of 5, and we want to calculate the 95% confidence interval…
64+(1.96)(5)=73.8
64-(1.96)(5)=54.2
Mean – Z Score – Standard Deviation – 1.96 for 95%
Correlations
Positive or Direct Correlation – change in same direction
Negative or Indirect Correlation – change in opposite direction
Correlations range from -1 to +1
The Absolute value of the correlation represents the strength of the correlation
Strong Correlation =...

...Stem-and-leaf displays and dot plots are useful for detecting
Student Answer:
Outliers
Skewness
Midpoint of data
All of the above
Points Received: 1 of 1
Comments:
4. Question : When a population is skewed to the left or right with a very long tail, what is the best measure to use for central tendency.
Student Answer: Population mean
Population mode
Population median
Population standard deviation
Points Received: 1 of 1
Comments:
5. Question : The science of using a sample to make generalizations about the important aspects of a population is known as
Student Answer: Statistical Process Control.
Descriptive Statistics.
A random sample.
Statistical Inference.
Points Received: 1 of 1
Comments:
6. Question : The standardized value of any value in a population or sample is called
Student Answer: percentile
coefficient of variation
quartile
Z-score
Points Received: 1 of 1
Comments:
7. Question : It is appropriate to use the Empirical Rule to describe a population that is extremely skewed.
Student Answer: True
False
Points Received: 1 of 1
Comments:
8. Question : The population mean is the average of the population measurements.
Student Answer:
True
False...

...Statistics 1
BusinessStatistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about businessstatistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that businessstatistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from businessstatistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s...

...
Final Project: Nyke Shoe Company
Barbara Greczyn
STA 201 - Principles of Statistics
Instructor Alok Dihtal
April 26, 2015
Introduction
Nyke Shoe Company has been in business for over 50 years. Over the last five years, the company has been undergoing some financial hardship due to an erratic market and an inability to understand what the consumer actually needs. In a last ditch effort to avoid bankruptcy, they have adopted a newbusiness model which entails the development of only one shoe size. In order to achieve this goal, statistical data must be utilized and applied to make the best choice. The data used will be explained to the fullest and a conclusion will be then obtained.
Methodology
A sample group of 35 participants was gathered, 18 females and 17 males. Their heights and shoe sizes were gathered and their data was processed in three categories: shoe size, height, gender. Descriptive statistics was applied to three separate data sets, one with all participants included, one sets with just female participants, and one with just male participants. Then a two sample t-test was conducted with the assumption that there were unequal variances amongst both male and female data sets.
Results
There is a normal distribution of the data with ranges in size from size 5 to size 14 amongst the participants. With these ranges, the mean is 9.142, with a standard deviation of 2.583...