SECTION-A (18 Marks)
| |Select the correct answer. Cutting or over writing is not allowed. | | | |If in a table all possible values of a random variable are given with their corresponding probabilities, then its table is called as | | | |(a) Prob. Density function (b) Dist. function (c) Prob. Distribution (d) Continuous dist. | | | |A variable that can assume all possible values between two points is called.. | | | |(a) Discrete variable (b) Random variable | | | |(c) Continuous random variable (d) discrete sample space | | | |A formula or equation used to represent the probability distribution of a continuous random variable .. | | | |(a) Prob. Density function (b) Dist. function (c) Prob. Distribution (d) Continuous dist. | | | |If X is random variable and f(X) is the probability of X then the expected value of this random variable is equal to: | | | |(a)(f(X) (b) ([X+ f(X)] (c) (f(X) + X (d) (Xf(X) | | | |Which of the following is not possible in probability distribution | | | |(a) P(X) > 0 (b) (P(X)=1 (c) (XP(X) = 2 (d) P(X) = -0.5 | | | |If C is a constant in a continuous probability distribution, then P( X=C) is always equal to: | | | |(a) Zero (b) One (c) negative (d) impossible | | | |E [X – E(X)] is : | | | |(a) E(X) (b) 0 (c) Var(X) (d) S.D.(X) | | | |E [X – E(X)]2 is : | | | |(a) E(X) (b) E(X2) (c) Var(X) (d) S.D.(X) | | | |In a discrete probability distribution the sum of all the probabilities is always equal to | | | |(a) Zero (b) One (c) Minimum (d) Maximum | | | |The total area under the curve of a continuous probability density function is always equal to | | | |(a) Zero (b) One (c) -1 (d) None of them | | |...

...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
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...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...

...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...

...1. A density curve consists of a straight line segment that begins at the origin (0, 0) and has
slope of 1.
a. Sketch this density curve. What are the coordinates of the right endpoint of the segment?
(Note that the right endpoint should be fixed so that the total area under the curve is 1.
This is required for a valid density curve.)
b. Determine the median, the first quartile (Q1), and the third quartile (Q3).
c. Relative to the median, where would you expect the mean of the distribution to lie?
Explain briefly.
The distribution is skewed left, so the mean will be left of the median.
d. What percent of the observations lie below 0.5? Above 1.5?
2. The following are the salaries of employees in a small business:
15,000 15,000 17,500 23,500 23,750 25,000 26,000 27,500 29,000 45,000
a. Before using your calculator, do you think that the mean or the median for these values
will be higher? Why do you think so?
b. What are the mean and median of the salaries? Was your answer to (a) correct?
c. Find the standard deviation and the IQR of the data
d. Describe the shape of the distribution terms of its overall shape, including outliers and
skewness. Be sure to give the locations of the main features
e. Speculate on the reasons for why the distribution is shaped as it is.
3. The following represents the outcomes of rolling a die 600 times (actually, it was
simulated on the TI83 as follows: RandInt (1,6,600)_L1).
Face
1
2
3 ...

...Stats: Modeling the World - Bock, Velleman, & DeVeaux
Chapter 1: Stats Starts Here Chapter 2: Data
Key Vocabulary:
Statistics data, datum variation individual respondent subject participant experimental unit observation variable
categorical quantitative
Calculator Skills:
enter data in a list change a datum
delete a datum name a new list clear a list delete a list
recreate a list copy a list
1. Name three things you learned about Statistics in Chapter 1.
2. The authors claim that this book is very different from a typical mathematics textbook. Would you agree or disagree, based on what you read in Chapter 1? Explain.
3. According to the authors, what are the “three simple steps to doing Statistics right?” 4. What do the authors refer to as the “W’s of data?” 5. Why must data be in context (the W’s)?
6. Explain the difference between a categorical variable and a quantitative variable. Give an example of each.
Chapter 1: Stats Starts Here / Chapter 2: Data
Stats: Modeling the World - Bock, Velleman, & DeVeaux
Chapter 3: Displaying and Describing Categorical Data
Key Vocabulary:
frequency table relative frequency table distribution bar chart pie chart contingency table marginal distribution conditional distribution independent segmented bar chart
Simpson’s Paradox
1. According to the authors, what are the three rules of data analysis?
2. Explain the difference between a frequency...

...1. Introduction
This report is about the case study of PAR, INC. From the following book: Statistics for Business an Economics, 8th edition by D.R. Anderson, D.J. Sweeney and Th.A. Williams, publisher: Dave Shaut. The case is described at page 416, chapter 10.
2. Problem statement
Par, Inc. has produced a new type of golf ball. The company wants to know if this new type of golf ball is comparable to the old ones. Therefore they did a test, which consists out of 40 trials with the current and 40 trials with the new golf balls. The testing was performed with a mechanical fitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the design. The outcomes are given in the table of appendix 1.
3. Hypothesis testing
The first thing to do is to formulate and present the rationale for a hypothesis test that Par, Inc. could use to compare the driving distance of the current and new golf balls. By formulation of these hypothesis there is assumed that the new and current golf balls show no significant difference to each other. The hypothesis and alternative hypothesis are formulated as follow:
Question 1
H0 : µ1 - µ2 = 0 (they are the same)
Ha : µ1 - µ2 ≠ 0 (the are not the same)
4. P-value
Secondly; analyze the data to provide the hypothesis testing conclusion. The p-value for the test is:
Question 2
Note: the statistical data is provide in § 5.
-one machine
-two...

...H0: µ=12 vs Ha: µ≠12. If the value of the test statistic is -1.73 based on a sample of size 20, what type of test statistic is it and what is the corresponding p-value?
a. z statistic; 0.0287
b. z statistic; 0.0574
c. t statistic; approximately 0.10
d. t statistic; approximately 0.05
12. The diameter of 3.5 inch diskettes is assumed to be normally distributed. The quality control inspector conducted a hypothesis test to examine the average diameter of diskettes. He used a sample of size 35 and the following null and alternative hypotheses: H0: = 3.5 vs Ha: ≠ 3.5. At α=0.05, he rejected the null hypothesis. Which one of the following statements is true if it is assumed that he/she performed the test correctly?
a. The 95% confidence interval constructed by the sample did not contain 0
b. The 95% confidence interval constructed by the sample did not contain 3.5
c. The absolute value of the test statistic is less than 1.96
d. The p-value is greater than 0.05
13. The sales of DVD players at Venus music store were studied, and the probability distribution is shown in the following graphical representation. If X is a random variable denoting the number of DVD players sold in a week, then the mean number of DVD players sold in a week is:
a. 0.6
b. 1.0
c. 1.5
d. 2.0
14. In testing H0: µ1 - µ2 = 0 against Ha: µ1...

...central tendency of the sample.
6. Measures of dispersion: range, the interquartile range, the variance, and the standard deviation. What do these measures tell you about the “spread” of the data? Why is it important to spend time performing basic descriptive statistics prior to conducting inferential statistical tests?
Variance of a sample = S2 = =
Standard Deviation of sample S=
Range is the difference between the highest and the lowest values (250-100) = 150
Interquartile Range takes into consideration the fact that there are data extremes that affect the range. In the case of the data above, most of the values are around the median but two values (250 and 275) are extremes. In this scenario, Interquartile range is a better indication of the dispersion of the distribution
100 100 103 104 105 Q1 107 110 110 114 115 M 115 115 115 115 117 Q2 117 118 120 250 275
• Q1 = (105+107)/2 = 106
• Q2 = (117+117)/2 = 117
• IR = 117-106 =9
It is important to evaluate data and look at the entire picture to determine whether something fits or does not. The fact that we get two measurements that were extreme might be an indication that something may have gone wrong. Descriptive statistics in such a case becomes instrumental in our analysis
Type I and Type II Error: The concept of Type I and Type II Error is critical and will come into play with each statistical test you perform. Discuss the implications of...

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