Stats 260 [A01] & [A02]
[3]
Midterm 1
October 2013
1. The data given below are seven temperature readings reported in degrees Celsius.
15 , 23 , -18 , 19 , 26 , -5 , 12
The temperatures are converted into the Kelvin scale by adding 273.16. Determine
which
Resta, Mack
STAT 255 R Assignment 1
1)
4
0
2
Frequency
6
8
Histogram of August
2
4
6
8
10
12
14
16
August
6
4
2
0
Frequency
8
10
Histogram of October
20
30
40
October
50
August<c(7.5,7.2,3.0,12.1,15.1,12.1,11.5,11.8,7.2,13.2,13.6,8.2,9.5,8.4,13.3,12.5,12.
Stat 255 Set 25
Comparing Two Means
This section concerns itself with the methods used to compare two sets of sample data to
determine if there is a difference between two population means.
Expectation and Variance
Comparing Two Independent Means
Just as
Faculty of Science | Department of Mathematics and Statistics
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Extra problem solutions set 19-22.
1
Set 20
1. Let X be the dissolve time of a particular produce in gastric juice; X Normal.
(a) = the true average time it takes to dissolve a particular product in gastric
juice.
(b) H0 : 45 seconds (the true average dis
Stat 255 Set 13-14
1
Continuous Random Variables
Continuous Random Variables
A continuous random variable is a random variable that can take on an uncountably
infinite number of possible outcomes. The ability of the variable to take any value makes
the pr
Extra problem solutions set 11-14.
1
Set 11
1. (a) Let X = the number of times that the yield has improved (out of 10 trials).
X Binomial(n = 10, p = 0.70), P (X 6) = 0.3504 (tables)
(b) V (X) = 2.1 improvements2
(c) E(X) = 7 improvements
2. (a) Let X = t
Extra problem solutions set 23-24.
1
Set 23
1. (a) d = 0.03 or 3%
(b) d = 0.035 or 3.5%
2. (a) (0.51, 0.73)
(b) n = 709
(c) Let X be the number of newtrophils out of 100 white cells; X Binomial(n =
100, p =?)
i. p = the true proportion of neutrophils out
Stat 255 Set 23
Determining Sample Size
To determine the sample size needed to obtain a confidence interval of a certain width
you can you use these two formulas. Where d= width/2
or
1. The branch manager of an outlet (Store 1) of a large nationwide chain
Extra problem solutions sets 25-26.
1
Set 25 and 26
1. (a)
i. m = true average tarsus length of males, f = true average tarsus length
of females
ii. H0 : m = f , HA : m 6= f (two-sided)
iii. Assume variances are unequal, Zobs = 3.828
iv. Standard Normal,
Fraction Calculations
- A decimal number, variable, or exponent cannot be
entered as a fraction.
Coordinate Conversions
- Before performing a calculation, select the angular unit.
(See page 6)
Entered data are kept In memor
Stat 255 Set 24
Comparing Population Proportion from
Two Separate Samples
When we are interested in comparing the proportions associated with two populations from which we
have selected independent samples from each population, we use the difference betwe
Extra problem solutions set 27
1
Set 27
1. n = 25 in each group
2. n = 213 in each group
3. n = 313 in each group
4. (a) (-0.17, 11.37)
(b)
i.
ii.
iii.
iv.
v.
D = true average difference in blood glucose levels (before - after)
H0 : D 0, HA : D > 0 (one-s
Homework Assignment Sets The textbook for Statistics 255 is the third edition or second edition of Statistical Methods
in the Biological and Health Sciences by J. Susan Milton. Whenever the identification number of an assigned exercise in
the third editio
Stat 255 Set 11
1
Binomial Random Variables
Binomial Experiment.
The experiment has a fixed Number of Trials.
Each trial results in either Success or Failure.
The probability of success remains constant for each trial.
All trials are independent.
Then
Stat 255 Set 21
Type I and Type II Errors
Power:
1
1 SAMPLE SIZE CALCULATION
1
2
Sample Size Calculation
Sample Size Calculations
Example:
A consumer group wants to estimate the mean electric bills for the month of July for
single-family homes in a large
Stat 255 Set 17
1
Central Limit Theorem
Intuition
Central Limit Theorem
Example
1
2 HOMEWORK
More on Expectation
Standard Error of X
2
Homework
Complete section 14.14 and 14.15 of the course handbook.
2
Stat 255 Set 12
1
Poisson Random Variables
Poisson Experiment:
The number of successes that occur in any interval is independent of the number
of successes that occur in any other interval.
The probability of a success in an interval is the same as for
Stat 255 Set 8
1
Random Variables
A random variable is a variable that assigns a numerical result to an outcome of an
event that is associated with chance. (Ex. The number of heads when you flip a coin 5
times).
Random variables can either be discrete or
SET 22
INFERENCES ON PROPORTIONS
A Populations Proportion is a statistic that represents the number of objects in a population that
have a particular trait.
P=X
N
where X denotes the # with trait
and N denotes the total # in the population
When we take a
Stat 255 Set 27
Comparing Two Population Means: Matched Pairs Experiments
Experiments in which observations are paired and the differences are analyzed are called matched pairs
experiments. The idea is to compare population means by comparing the differen
Stat 255 Set 15 and 16
1
Normal Approximation to the Binomial
Let X B(n, p). When n is large and p is close to 0.5 then the Normal distribution is
remarkably close to the Binomial distribution.
R Example
Normal Approximation to the Binomial
Conditions for
Stat 255 Set 7
1
Bayes Theorem
In this lesson, well learn about a classical theorem known as Bayes Theorem. In short,
well want to use Bayes Theorem to find the conditional probability of an event P (A|B),
say, when the reverse conditional probability, P
Stat 255 Set 9
1
Expected Value
Interpretation
Given a random variable, X, the expected value of X is intuitively, the long-run average
value of repetitions of the experiment it represents. If we do an experiment over and
over again the expected value of
Stat 255 Set 9
1
Expected Value Rules and Variance
The Fundamental Expectation Rule
Variance
Expectation and Variance Rules
1
1 EXPECTED VALUE RULES AND VARIANCE
2
.
Example: Let X and Y be independent random variable with E(X) = 10, E(Y ) = 16,
V (X) = 2
Extra problem solutions set 15-18.
Set 15
X
f (x)
1. X = the number of successes in n trials
0
0.7
1
0.3
0.3
0.4
0.5
0.6
0.7
2. Plot of f (x) vs X
f(x)
1
0.0
0.2
0.4
0.6
0.8
1.0
x
3. First we look at all possible samples of size 2 from this distribution.
Stat 255 Set 18
1
Confidence Intervals
We know from last class that for a distribution with mean and standard deviation ,
if:
1. The underlying distribution is Normal,
or
2. The sample size is greater than 25 (n > 25)
then
N (, )
X
n
allows us to make s
Stat 255 Set 19-20
1
Hypothesis Testing
A hypothesis test is conducted by observing a process that is modelled via a set of
random variables. A hypothesis test is a method of statistical inference. A hypothesis
is proposed for a population parameter of a