2.2 Organizing Data
When data is collected, in its original form it is called raw data.
Raw data is often organized into tables called frequency distributions.
The frequency tells how many data points are in a category.
The total of all frequencies gives
Stat 130
Chapter 2, 3 Classwork
1. Complete the table below:
Classes
14.3-14.8
14.9-15.4
15.5-16.0
16.1-16.6
16.7-17.2
Frequency
4
2
6
3
5
Relative freq.
Cumulative freq.
Use the table above to complete the following:
a. the class width is _
b. the upper
Chapter 8 Classwork
Use the 5-step method to test each claim. Also report the pvalue (or range of values) associated
with each test.
1. A tire dealer claims that the mean lifetime of a certain tire is at least 39,000 miles, with a
standard deviation of 12
Chapter 1
The Nature of Probability and Statistics
The subject matter of Statistics essentially is concerned with how best to do the following:
1.
2.
3.
Collect data (experimental design)
Summarize data (descriptive statistics)
Draw conclusions on the bas
Chapter 4 - Probability
4.1 Fundamentals
Experiment well-defined process that produces outcomes
Event any collection of outcomes of a procedure
Simple event a single outcome
Sample space all possible simple events
1.
experiment: toss a coin once; event: c
Binomial Distributions
For each of the following, identify n, x, p, and q. Then use the binomial formula to find the
probability.
1. A genetic trait of one family manifests itself in 25% of the offspring. If eight offspring
are randomly selected, find the
8.4 Tests on a Population Proportion
Assumptions:
1. The conditions for a binomial distribution are satisfied.
2.
The sample is large enough to use the normal distribution if both np 5 and
nq 5.
p = population (true) proportion used in the hypotheses
p =
8.3 t-Test for a Mean
In reality, the population standard deviation () is almost never known. In most cases, the t or
student distribution is used.
We will apply the same rules to hypothesis testing. The five steps remain the same with these
two exception
8.1,2 Hypothesis Tests
There are 2 types of hypotheses:
a.
null hypothesis (H0) a statement of no change or difference;
contains: =, , or . The null hypothesis is assumed to be true unless there is
strong evidence to suggest that it is not.
b.
alternative
7.3 Estimating a Population Proportion
Assumptions:
1.
The conditions for a binomial distribution are satisfied.
2.
The sample is large enough to use the normal distribution if np 5 and nq 5.
(Since the value of p is unknown, we use the sample proportion,
Classwork Probability
1. In a survey of college students. 809 said they have cheated on an exam and 1793 said
they have not. If one student is selected at random, find the probability that the student
has cheated on an exam.
2. The data in the table repre
Operations on Events
S = cfw_3, 4, 5, 6, 7, 8
A = cfw_3, 5, 7
B = cfw_4, 5, 6
C = cfw_8
A or B = A union B
= cfw_all outcomes in either A or B
= cfw_combined outcomes
=
A or C =
A and B = A intersect B
= cfw_all outcomes in both A and B
= cfw_outcomes in
2.3 Histograms
A histogram is similar to a bar graph, but there are no spaces between
the bars. Each bar represents a class of data and the height of each bar
is the frequency of that class. The horizontal scale may show classes,
class boundaries or clas
Stem-and-leaf Plots
Stem-and-leaf plots or stemplots are a method for showing the frequency with which certain
classes of values occur. You could make a frequency distribution table or a histogram for the
values, or you can use a stem-and-leaf plot and le
Chapter 3
Data Description
Measures of center
Measures of variation
Measures of relative standing
3-1 Measures of Center
1.
Mean (arithmetic mean or sample mean)
x
2.
x
i
n
Median (MD) The measure in the center when data is arranged in order.
Find the
Chapter 1
Introduction to Statistics
Statistics is the science of collecting, organizing, summarizing, and analyzing information to
draw conclusions or answer questions. In addition, statistics is about providing a measure of
confidence in any conclusions
Review 2 Solutions
1. a) 13/52 = or .25
b) 13/52 + 13/52 = or .5
c) 13/52 + 4/52 1/52 = 16/52 or .31
d) 13/52 + 12/52 3/52 = 22/52 or .42
2. a) (4/12)(3/11) = 1/11 or .09
b) (8/12)3 = 8/27 or .296
c) P(at least one dead) = 1 P(no dead) = 1 P(all three are
Stat 130
Review Chapters 6 and 7
1. Find the area under the standard normal curve:
a.
b.
c.
d.
e.
f.
to the left of 3.12
to the right of -1.33
above 1.76
below 2.05
between 2 and 3
between 1.9 and 2.7
2. Find the value of z if:
a.
b.
c.
d.
e.
f.
g.
the ar
Review 1 Solutions
1. a) 6.5
b) 8
c) 6.5 d) 7
e) 10 f) 9.1 g) 3.0 h) z =
7 6.5
= .17
3.0
i) 6.5 2(3.0) 6.5 6.0 .5 to 12.5 or (.5, 12.5)
j) At least or 75% of the data; at least 8/9 or 89% of the data
k) 95% of the data should fall into this interval IF it
Stat 130
Test 1 Review
Chapter 1
Know the difference between:
a. parameter and statistic
b. qualitative and quantitative
c. discrete and continuous
Be able to classify data:
Level
Nominal
(categories,
labels)
Ordinal
(ratings, rankings)
Interval (measure
7.2 Estimating a Population Mean:
Not Known
In reality, the population standard deviation is
almost never known. Most estimates of the mean
are done as outlined in this section.
Take a sample of size n.
2. Collect sample data.
3.
Find the value of x and
6.2 Application of Normal Distributions
There are many variables in the world that are normally distributed. It would not be
feasible to make a table for every one of them. We convert to z-scores and use the
standard normal table.
z=
xx
s
z=
x
Finding pro
6.1 Normal Distributions
In this chapter, we will work with continuous random variables.
A density curve is a graph of a continuous probability distribution. It has the
following properties:
1. The total area under the curve is 1 (100%)
2. The curve does