Practice Problems 1-KEY 1. The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 8 83 9 82 10 86

For the above sample, compute the following measures. a. b. c. The mean = ∑X/n = 860/10 = 86 The median = (85+86)/2 = 85.5 The variance = ∑ X - X 2/ n-1 = {(84-86)2 + (87-86)2 + (84-86)2 + (88-86)2 + (85-86)2 + (90-86)2 + (91-86)2 + (83The standard deviation = √8.89 = 2.98 The coefficient of variation = 2.98/86 * 100% = 3.47%

86)2 + (82-86)2 + (86-86)2 } / (10 -1) = 8.89 d. f.

2. In 2008, the average age of students at GUST was 22 with a standard deviation of 3.96. In 2009, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer. CV2008 = 3.96/22 * 100% = 18% CV2009 = 4.08/24 * 100% = 17% So, 2008 shows more dispersed distribution 3. A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of examinations are selected at random and scored. The results are shown below. Grade For the above data, determine a. The mean = ∑X/n = 664/8 = 83 b. c. The median = (85+87)/2 = 86 The standard deviation = √variance ariance = ∑ X - X 2/ n-1 = {(93-83)2 + (65-83)2 + (80-83)2 + (97-83)2 + (85-83)2 + (87-83)2 + (97-83)2 + (60 - 83)2 } / (8 -1) = 196.29 S0, standard deviation = √196.29 = 14.01 d. The coefficient of variation = 14.01/83 * 100% = 16.88% 93 65 80 97 85 87 97 60

4. The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product. Daily Supply (y) Unit Price (x) 5 2 7 4 9 8 12 5 10 7 13 8 16 16 16 6

...techniques.
Firstly we look at data analysis. This approach starts with data that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and 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...

...
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...

...compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve 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’...

...QUESTION 21
The finishing process on new furniture leaves slight blemishes. The table below displays a manager's probability assessment of the number of blemishes on one piece of new furniture.
Number of Blemishes
0
1
2
3
4
5
Probability
0.34
0.25
0.19
0.11
0.07
0.04
1. On average, how many blemishes do we expect on one piece of new furniture?
2. What is the variance of blemishes on one piece of new furniture? (round to the nearest hundredth) QUESTION 22
The probability that a person catches a cold during the cold-and-flu season is 0.4. Assume that 10 people are chosen at random.
On average, how many of these ten people would you expect to catch a cold?
What is the standard deviation of the number of people who catch a cold? (round to the nearest hundredth)
QUESTION 23
The number of nails in a five-pound box is normally distributed with a mean of 566 and a standard deviation of 33.
What is the probability that there are less than 500 nails in a randomly-selected five-pound box of nails? (express as a decimal, not a percentage)
The probability is 0.99 that a randomly-selected five-pound box of nails contains at least how many nails approximately?
QUESTION 24
You are the owner of a small casino in Las Vegas and you would like to reward the high-rollers who come to your casino. In particular, you want to give free accommodations to no more than 10% of your patrons....

...Pakistan International School Riyadh
Class XII
1. How many possible permutations can be formed from the word ‘statistics’?
2. In how many ways can a team of 11 players be chosen from a total of 16 players?
3. State multiplicative theorem of probability for dependent events.
4. An aptitude test with 4 options. If a student marks the options of the questions randomly and independently, then find the probability of being correct to 4questions.
5. A can solve 75% questions in a book and B can solve 60% questions in that book. Find the probability that randomly selected questions is solved by them?
6. What is the probability of getting at least 2 heads when 3 coins are tossed?
7. Find P(A ∩ B) if P(A) = ¼ and P(B) = 1/3 and p(A U B) = ½ .
8. State the laws of expectation.
9. Describe the properties of discrete probability distribution.
10. Given E(X) = 0.55, Var(X) = 1.55 and Y = 2X + 1. Find E(Y) and Var(Y).
11. Show that the mean of the binomial distribution (q + p)2 is 2p.
12. Show that mean is 2p and σ2 = 2pq for a binomial distribution in which n = 2.
13. A random variable X has a binomial distribution with E(X) = 2.4 and p = 0.3. Find the standard deviation of X.
14. Describe the normal distribution and write down its equation.
15. What is standard normal variable?
16. The value 2nd moment about mean in a normal distribution...

...Time | Contributor | Contribution |
Ancient Greece | Philosophers | Ideas - no quantitative analyses |
17th Century | Graunt,Petty
Pascal, Bernoulli | studied affairs of state, vital statistics of populations studied probability through games of chance, gambling |
18th Century | Laplace, Gauss | normal curve, regression through study of astronomy |
19th Century | Quetelet
Galton | astronomer who first applied statistical analyses to human biologystudied genetic variation in humans(used regression and correlation) |
20th Century (early) | PearsonGossett (Student)
Fisher | studied natural selection using correlation, formed first academic department of statistics, Biometrika journal, helped develop the Chi Square analysisstudied process of brewing, alerted the statistics community about problems with small sample sizes, developed Student's testevolutionary biologists - developed ANOVA, stressed the importance of experimental design |
20th Century (later) | Wilcoxon
Kruskal, Wallis
Spearman
Kendall
Tukey
Dunnett
Keuls
Computer Technology | biochemist studied pesticides, non-parametric equivalent of two-samples testeconomists who developed the non-parametric equivalent of the ANOVApsychologist who developed a non-parametric equivalent of the correlation coefficientstatistician who developed another non-parametric equivalent the correlation coefficientstatistician who developed multiple comparisons...

...Major Statistics Assignment
Mary Grace Rivero
050853639
CNUR860-011
Vaska Micevski
Friday, March 30, 2012
Major Statistics Assignment
This major statistics assignment will finally pull together everything that was learned in this course. The application of all content within this course will be incorporated to three different research scenarios. Within each scenario, hypothesis testing will be done, followed by a discussion of relevant descriptive statistics and finally, a discussion of the findings which includes nursing practice implications and research implications.
Research Scenario #1
In this research scenario, the researchers were interested in the following research question: “Is there a difference in nurses’ abilities to identify nursing skills that reflect knowledge of client centered care values of A) respect and human dignity B) consistency, continuity and timelessness of care or C) patient autonomy, patient voice and patient as decision maker.” To answer this research question, a hypothesis testing will be conducted followed by a discussion of the findings. The discussion of the findings will include a discussion of descriptive statistics, followed by nursing and research implications.
Hypothesis Testing
Step 1. The first step in hypothesis testing is to state the null and research hypothesis. The null hypothesis can be: “There is no...

...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...