Chapter 7
7.
108
754
646
999
861
933
290
201
602
641
292
531
10.
a) Infinite
b) Infinite
c) Finite
d) Infinite
e) Infinite
15.
a)
4376 45500/10=4550 is the point estimate mean
4798
5578
6446
2717
4119
4920
4237
4495
3814
b)
4376 4550-174
4798 4550 248
5578 4550 1028
6446 4550 1896
2717 4550-1833
4119 4550-431
4920 4550 370
4237 4550-313
4495 4550-55
3814 4550-736
9068620/10=906862
√906862=952.29
43.
a) Mean=6883 Standard deviation=2000
2000/√50=282.84
b) 6883-300=65386883+300=7183
6538-6883=-3457183-6883=300
-345/(2000/√50)=-1.22 300/(2000/√50)=1.06
-1.22=0.11121.06=0.8554
.8554-.1112=.7442Probability
c)
2000/√50=282.84
7500-6883=617/282.84=2.18=.9854
1-.9854=.0146 Probability
45.
a) 14,16
14-15=-1/(4/√60)=-1.94 16-15=1/(4/√60)=1.94
-1.94=0.97381.94=0.0262
0.9738-0.0262=0.9476Probability
b)
45/60=.75
-.75+15=14.25.75+15=15.75
14.25-15=-.75/(4/√60)=-1.45 15.75-15=.75/(4/√60)=1.45 -1.45=0.92651.45=0.0735
0.9265-0.0735= 0.853Probability
52.
a)
.40/√380=.0205
√.40(1-.40)/380=.0251
.40+.04=.44 .40-.04=.36
.44-.36=.08/.0251=3.19
b)

Chapter 8

3.
a)
n=60 standard deviation=15 mean=80 CI=.95
1-.95=.05/2=.025
80+1.96(15/√60)=83.8 80-1.96(15/√60)=76.2
b)
1-.95=.05/2=.025
80+1.96(15/√120)=82.6880-1.96(15/√120)=77.32
c) The effect of a larger sample size on an interval estimate caused the minimum population to go up and the max population went down.

16.
n=100 standard deviation=8.5 mean=49 CI=.95
1-.95=.05/2=.025
8.5/√100=.85 standard error
100-1=99 degrees of freedom
t-score= 1.984
a)1.984*.85=1.68
b)49-1.68=47.3249+1.68=50.68
c) The pilot for continental airlines flies no less than 47 hours ,which is higher than the pilots from united airlines who average just 36 hours. One reason that the labor costs are high could be due to the number of pilots they have on payroll. If pilots average 36...

...I. SampleSize Calculation (Calculated by Hand Only)
Example 9.65 Pg. 297
The Chevrolet dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the population proportion is believed to be no more than 0.15, how many owners must be included in a simple random sample if the dealers want to be 90% confident that the maximum likely error will be no more than 0.02?
Given Data
π = 0.15 = 15%
z = 1.645 (90%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.02
Formula
z² π (1- π)
E²
Solution
1.645²0.15 (1- 0.15)
0.02²
N = 862.55 => 863 (Always Round Up)
Example 9.63 Pg. 297
A national political candidate has commissioned a study to determine the percentage of registered voters who intend to vote for him in the upcoming election. To have 95% confidence that the sample percentage will be within 3 percentage points of the actual population percentage, how large a simple random sample is required?
Given Data
π = 0.5 = 50% *Use 0.5 or 50% when the percentage is not expressed in the problem.
z = 1.96 (95%) *Z-Score: 99% = 2.56; 95% = 1.96; 90% = 1.645
E = 0.03
Formula
z² π (1- π)
E²
Solution
1.96²0.50 (1- 0.50)
0.03²
N = 1067.11 => 1068 (Always Round Up)
...

...FINAL PROJECT STATISTICS
DENISE CAPALBO
Gender statistics is an area that cuts across traditional fields of statistics to identify, produce and disseminate statistics that reflect the realities of the lives of women and men, and policy issues relating to gender.
Women can still wear men's shoes, but the size they are accustomed to will be labeled differently in the men's sizes. Although the shoesize is related to the length of your foot, the sizes do not follow a direct formula. Subtract 1 1/2 from your size, if you are a size 6. Therefore, your equivalent men's size would be a 4 1/2.
Above is a dot graph showing the female comparison if she was to convert to a male shoe by length. It is a difference in length by a size and a half. This decision by Nyke is not a good company decision because as you can see based on the female to male conversion that the size difference is significantly larger for women due to the difference in foot length determines the size of shoe.
Europe | 35 | 35½ | 36 | 37 | 37½ | 38 | 38½ | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46½ | 48½ | Europe |
Mexico | | | | | | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 9 | 10 | 11 | 12.5 | Mexico |
Japan | M | 21.5 | 22 | 22.5 | 23 | 23.5 | 24 | 24.5 | 25 | 25.5 | 26 | 26.5 | 27.5 |...

...Calculating SampleSize
Types of Samples
Subjective or Convenience Sample
- Has some possibility of bias
- Cannot usually say it is representative
- Selection made by ease of collection
Simple Random Sample
- No subjective bias
- Equal chance of selection; e.g., select the fifth chart seen on every third day
- Can usually be backed to say it is representative
Systematic Sample
- Is a random sample
- Equal chance of selection due to methodology; e.g., computer-generated list of
random numbers, or every fifth name on a generated list
- Can usually be backed to say it is representative
Stratified Sample
- Breakdown the population into subgroups, then take a random sample from each subset
- Can usually be backed to say it is representative
SampleSize Calculation
The Automated Method
If you know your population size and desired confidence level you may use this Web-based calculator to automatically calculate samplesize.
The Manual Calculation Method
To perform samplesize calculation manually, you need the following values:
Population Value: Size of the population from which the sample will be selected. (Number of users or number of encounters)
Expected Frequency of the Factor under Study...

...3) n = 186, x = 103
A) 0.0643 B) 0.125 C) 0.00260 D) 0.0714
Find the minimum samplesize you should use to assure that your estimate of will be within the required margin of error around the population p.
4) Margin of error: 0.002; confidence level: 93%; and unknown
A) 204,757 B) 410 C) 204,750 D) 405
5) Margin of error: 0.07; confidence level: 95%; from a prior study, is estimated by the
decimal equivalent of 92%.
A) 58 B) 174 C) 51 D) 4
Use the given degree of confidence and sample data to construct a confidence interval for the
population proportion p.
6) When 343 college students are randomly selected and surveyed, it is found that 110 own
a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
A) 0.256 < p < 0.386 B) 0.279 < p < 0.362 C) 0.271 < p < 0.370 D) 0.262 < p < 0.379
Determine whether the given conditions justify using the margin of error E = when
finding a confidence interval estimate of the population mean .
7) The samplesize is n = 9, is not known, and the original population is normally distributed.
A) Yes B) No
Use the confidence level and sample data to find the margin of error E.
8) Systolic blood pressures for women aged 18-24: 94% confidence; n = 92,
x = 114.9 mm Hg, = 13.2 mm Hg
A) 47.6 mm Hg B) 2.3 mm Hg C) 2.6 mm Hg D) 9.6 mm Hg
Use the confidence level and...

...Final Examination
Name: Course:
Date:
Final Examination in Statistics (M.A.Ed./M.A.N.)
1.The scores of 15 masteral students in Statistics were 80,85,78,90,91,98,95,98,95,74,71,72,98,99,and 87. Find the measures of central tendency, the range, the variance, and the standard deviation.
2. In the performance evaluation of teachers, if the dean’s evaluation is given a weight of 5, self-evaluation is 2, peer’s evaluation is 2, and student’s evaluation is 1 and the teacher’s rating is 90, 95, 85, and 90, the mean rating of the teacher would be?
3. Compare the performance in the licensure examination of the two groups of graduates given below using mean and standard deviation. Also rank and interpret the results.
| |GROUP A |GROUP B |
|1 |98 |78 |
|2 |79 |95 |
|3 |78 |86 |
|4 |82 |88 |
|5 |82 |82 |
|6 |88 |99 |
|7 |89 |88 |
|8 |85 |76 |
|9 |88 |85 |
|10 |90 |82 |...

...Data’s that are fundamentally amalgamated into scopes of miscalculations, randomized sampling as well as certainty periods. Such thoughts like these are statistical by nature without us even realizing it. To further explain statistics, it is a discipline that is made up regarding certain factors that involve things like deductive reasoning; granted, Science is practically statistics in and of itself through fabricating experimentations that require data collectivity, recapitulating information for the purpose of understanding something and pulling deductions through the use of the Scientific Method (i.e. formulating theories) through data collection. Sample Data Sample data basically is a subclass of populations such as humans, animals and even objects; it often goes as far as Physical Science and the Scientific Method. Within statistics, known as survey methodology, Sample Data concerns itself in the selective method regarding the subset of inhabitants or humans from within any particular population. This is done in order to approximate the uniqueness of an entire populace like weight, gender, color, religion, job types, etc. Sample Data surveying is also extremely cost effective opposed to surveying an entire
population. In short, this form of Sample Data is, from my own opinion, nothing more than probability theories. Population Data On the other hand,...

...Transportation Survey Sample Calculation
The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. For example, if you use a confidence interval of 4 and 47% percent of your sample picks an answer you can be "sure" that if you had asked the question of the entire relevant population between 43% (47-4) and 51% (47+4) would have picked that answer.
The confidence level tells you how sure you can be. It is expressed as a percentage and represents how often the true percentage of the population who would pick an answer lies within the confidence interval. The 95% confidence level means you can be 95% certain; the 99% confidence level means you can be 99% certain. Most researchers use the 95% confidence level.
When you put the confidence level and the confidence interval together, you can say that you are 95% sure that the true percentage of the population is between 43% and 51%. The wider the confidence interval you are willing to accept, the more certain you can be that the whole population answers would be within that range.
For example, if you asked a sample of 1000 people in a city which brand of cola they preferred, and 60% said Brand A, you can be very certain that between 40 and 80% of all the people in the city actually do prefer that brand, but you cannot be so sure that between 59 and 61% of the people in the city prefer the brand....

...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 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...