Time spent on the internet per week follows a normal distribution with an average 13.5
hours per week and a standard deviation of 5.6 hours.
a) Can we assume a normal distribution of sample means?
b) What is the probability of a sample mean of 15 values b
A study is set up to determine the average remuneration earned by members of city council
in large cities. It is desired that the error from the mean is less than $5,000 with a 95% level
of confidence. It is estimated the least a council member is paid is
1.1 Sampling Methods
Section 1.1
Sampling Methods
STATISTICS
1
1.1 Sampling Methods
TYPE OF STATISTICS
DESCRIPTIVE
INFERENTIAL
Methods of organizing,
summarizing, and
presenting data in an
informative way.
Methods are used to
estimate the characteristics
1.1 Sampling Methods
Section 1.1
Sampling Methods
STATISTICS
The science of collecting,
organizing, presenting,
analyzing, and interpreting data
to assist in making more
effective decisions
1
1.1 Sampling Methods
TYPE OF STATISTICS
DESCRIPTIVE
INFERENTIAL
1.2 Frequency Distributions
Section 1.2
Frequency
Distributions
FREQUENCY DISTRIBUTIONS
GOAL: to organize raw data into a more meaningful form
RAW DATA: collected data that has not been organized
CLASS
FREQUENCY
REL. FREQ.
CUMUL. FREQ.
*Column headings va
1.2 Frequency Distributions
Section 1.2
Frequency
Distributions
FREQUENCY DISTRIBUTIONS
GOAL: to organize raw data into a more meaningful form
RAW DATA: collected data that has not been organized
CLASS
FREQUENCY
REL. FREQ.
CUMUL. FREQ.
*Column headings va
1.3 Measures of Central Tendency
Section 1.3
Measures of
Central Tendency
MEAN
: the entire group under study
: a subset of the population of interest.
x
x
n
X
N
=
x=
X, x =
N, n =
1
1.3 Measures of Central Tendency
Ex: 11 random students were surveyed to
1.3 Measures of Central Tendency
Section 1.3
Measures of
Central Tendency
MEAN
POPULATION: the entire group under study
SAMPLE: a subset of the population of interest.
POPULATION
X
N
sample
x
x
n
= Population Mean
x = sample mean
X, x = Individual Observ
A study is set up to determine the average remuneration earned by members of city council
in large cities. It is desired that the error from the mean is less than $5,000 with a 95% level
of confidence. It is estimated the least a council member is paid is
A Survey of 700 consumers shows that 500 purchase sugar-free gum regularly.
Contstruct a 95% confidence interval for the population proportion of customers who
regularly purchase sugar-free gum.
=
p=(
,
)
A market survey was conducted to estimate the prop
A Survey of 700 consumers shows that 500 purchase sugar-free gum regularly.
Contstruct a 95% confidence interval for the population proportion of customers who
regularly purchase sugar-free gum.
= 0.05
p = ( #
,
#
)
n = 700
x = 500
p-hat = 0.7142857
z =
In a recent survey of 200 people who taste tested a new kind cereal, 46 people said they would purchase it.
The manufacturer thought it would be worth while launching the new cereal if more than 20% of the
population would consider purchasing it.
a) Can w
In a recent survey of 200 people who taste tested a new kind cereal, 46 people said they would purchase it.
The manufacturer thought it would be worth while launching the new cereal if more than 20% of the
population would consider purchasing it.
a) Can w
Historically at Jamestown Steel Co. daily production of desks follows a normal
distribution with a mean of 200 and standard deviation of 16. A new production
method was recently introduced, and the company would like to know if there has
been a change in
Historically at Jamestown Steel Co. daily production of desks follows a normal
distribution with a mean of 200 and standard deviation of 16. A new production
method was recently introduced, and the company would like to know if there has
been a change in
Historically at Jamestown Steel Co. daily production of desks follows a normal
distribution with a mean of 200 and standard deviation of 16. A new production
method was recently introduced, and the company would like to know if there has
been a change in
A recent article in a magazine reported that a job awaits only 1 in 3 new college
graduates across Canada. A random sample of 200 recent Fanshawe
graduates revealed that 80 had jobs. At the .02 significance level, can we
conclude that Fanshawe has a large
A recent article in a magazine reported that a job awaits only 1 in 3 new college
graduates across Canada. A random sample of 200 recent Fanshawe
graduates revealed that 80 had jobs. At the .02 significance level, can we
conclude that Fanshawe has a large
In order to estimate the mean amount spent by all costumers, a retail chain surveyed
400 random purchases. The sample showed a mean purchase amount of $500 and a
standard deviation of $100. Establish a 99% confidence interval estimate of the mean
amount p
In order to estimate the mean amount spent by all costumers, a retail chain surveyed
400 random purchases. The sample showed a mean purchase amount of $500 and a
standard deviation of $100. Establish a 99% confidence interval estimate of the mean
amount p
1.5 Probability
Section 1.5
Probability
PROBABILITY ANALYSIS
PROBABILITY ANALYSIS allows us to:
EXPERIMENT:
EVENT:
SAMPLE SPACE: complete list or representation of all of
the possible outcomes of an
experiment
1
1.5 Probability
PROBABILITY
Dr. Millar owns
1.5 Probability
Section 1.5
Probability
PROBABILITY ANALYSIS
PROBABILITY ANALYSIS allows us to:
Estimate the chance of uncertain outcomes
Draw generally reliable inferences from sample data
EXPERIMENT: any activity with an uncertain outcome
EVENT: one or
1.6 And, Or, & Not
Section 1.6
And, Or, & Not
INDEPENDENT vs. MUTUALLY EXCLUSIVE
INDEPENDENT: Two events are independent
if, the probability of one is
unaffected by whether the
other event has occurred.
MUTUALLY EXCLUSIVE: Two events that cannot
happen at
Sampling Distributions of the Sample Mean
Math 1045
1. Suppose a population has a mean of 10 and a standard deviation of 3. What is the mean and
standard deviation for the sampling distribution of samples of size 25?
2. Suppose the mean house price in a c
The t-Distribution
Math 1045
1. Find the t-score for a t-distribution with 19 degrees of freedom and an area of 0.1 in the right
tail.
2. Find the t-score for a
t-distribution with 73
degrees of freedom
and an area of 0.05 in
both tails.
3. Find the t-sco
Sample Size-Means
Math 1045
1. The dean of a college wants to use the mean of a random sample to estimate the amount of
time students take to get from one class to the next and she wants to be able to assert with a
95% probability that her error will be a
Sample Size-Proportions
Math 1045
1. Suppose the provincial highway department wants to estimate what proportion of all trucks
operating between Toronto and London carry too heavy a load and it wants to assert with a
probability of 95% that its error will
Math 1045
Confidence Intervals-Means
1. A travel industry research company wants to estimate the average cost of a domestic trip for
businesses travellers. The company takes a random sample of 51 business travellers and finds
the average cost of a domesti