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 calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window.

We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99.

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?...

...
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.
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
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.
Descriptive Statistics: Mean, Median
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
Mean...

...terminologies have infrastructures in place to maintain and evolve
the terminologies across time. The NANDA, NOC, and NIC (N3) terminologies provide
comprehensiveness of terms, in that each includes terms to describe care in all types of settings.
Additionally, all have been developed through research involving literature review and the
extensive input of large numbers of nurses.
The rate of diffusion of a new language can be accelerated by defining a clear direction and
taking action. For example, usage of N3 in the 43 nursing programs in Michigan substantially
terminologies form a subset of SNOMED CT, the comprehensive clinical terminology. The
SNOMED CT terminology is recognized by the National Centers for Vital and Health Statistics
and the Consolidated Health Informatics Initiative as an acceptable standard for the Federal
Patient Medical Record Information effort80 and is an ANA recognized terminology.75 Though
nursing-specific terminology content is available in SNOMED CT, it is not the purview of
SNOMED CT to keep the content current. Rather, the responsibility falls to nursing entities
(terminology developers) to ensure that the quality and comprehensiveness of the terminologies
is sustained and improved across time.
The N3 terminology developers are already taking responsibility for ensuring that the c
The N3 terminology developers are already taking responsibility for ensuring that the content
is updated regularly,...

...modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as means, medians and standard deviations.
Uncertainty is a key aspect of most business problems. To deal with uncertainty, we need a basic
understanding of probability. Chapter 2 covers basic rules of probability and in Chapter 3 we
discuss the important concept of probability distributions in some generality.
In Chapter 4 we discuss statistical inference (estimation), where the basic problem is to estimate
one or more characteristics of a population. Since it is too expensive to obtain the population
information, we instead select a sample from the population and then use the information in the
sample to infer the characteristics of the population.
In Chapter 5 we look at the topic of regression analysis which is used to study relationships
between variables.
In Chapter 6 we study another type of decision making called decision analysis where costs and
proﬁts are considered to be important. The problem is not whether to accept or reject a statement
but to select the best alternative from a list of several possible decisions. Usually no...

...
Contents
Question 1 3
Question 2a 5
Question 2b 6
Question 2c 7
Question 3a 8
Question 3b 8
Question 3c 10
Question 3d 11
Question 4 12
Question 5 14
References 15
Question 1
The sampling method that Mr. Kwok is using is Stratified Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean...

...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
DescriptiveStatistics: 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. |...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...

...problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.
A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’
In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.
DATA COLLECTION METHODS
Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’ Government School.
The marks were divided into the form:
Mathematics Marks, x
Mental Mathematics marks, y
DATA PRESENTATION AND ANALYSIS
Sample number
Marks earned (x)
x²
1
70
4900
2
86
7396
3
49
2401
4
66
4356
5
94
8836
6
68...

...Statistics Vocabulary
Chapter 1
Data are collections of observations ( such as measurements, genders, survey responses)
Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusion based on the data
A Population is the complete collection of individuals (scores, people, measurements and so on) to be studied. The collection is complete in the sense that includes ALL of the individuals to be studied
A census is the collection of data from EVERY member of the population
A sample is a subcollection of member selected from a population
A Parameter is a numerical measurement describing some characteristic of a population
A statistic is a numerical measurement describing some characteristic of a sample
Quantitative (or numerical) data consist of numbers representing counts or measurements
Categorical (or qualitative or attribute) data consist of names or labels that are not numbers representing counts or measurements
Discrete data result when the number of possible values is either a finite number or a “countable” number. (That is, the number of possible values is 0 or 1 or 2 and so on
Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
The nominal level of measurement is characterized by data...