STEPS TO HELP FOCUS ON PROBLEM TYPE.
1. Read the problem statement several times and try to visualize the “real”
situation and exactly what you are interested in doing.
a. Visualize (define) the population (or process) being talked about. Can you
explain this population to a friend (in your own words)
b. What are the parameters of the population that makes that population unique
from other populations (population mean, population proportion, etc.)
c. When you start to take samples from the population, what is the random
variable that describes the outcome? Write down several possible values for
this random variable so you can determine if you are dealing with continuous
or discrete data.
d. What is it about the population that you want to do? Normally, at this level
you would want to either estimate some parameter of the population (point
estimate or confidence interval estimate) or test some hypothesis about the
population. The main structures we study in this course are single mean,
difference in means, single proportion, difference in proportions, etc.
e. When you take your sample, what “statistics” will you calculate? (sample
mean, sample z-score, sample proportion, difference in two sample means,
etc.)
f. After all this, you will need to determine the appropriate statistical method to
use when you analyze the data to answer question 1.d. above.
2. The appropriate statistical tool will be influenced by the following factors.
a. Is the population you are sampling from represent a continuous random
variable with approximately a normal distribution or some other structure
(proportions)?
b. Is the sample size “large” or “small”?
c. Is the population standard deviation known or unknown (for problems
dealing with continuous random variables)?
d. Depending on the answers to these questions, for this course you will be
forced into one of the following structures.
*Large sample estimation (point estimate and confidence interval
estimate) of population mean when population sigma known (will use
known σ and z tables) – normality assumption for population not normally
needed here.
* Large sample estimation (point estimate and confidence interval
estimate) of population mean when population sigma unknown (will
use sample standard deviation, s, to estimate σ and z tables) – normality
assumption for population not normally needed here.
*Small sample estimation (point estimate and confidence interval
estimate) of population mean when population sigma known (will use
known σ and z tables) – normality assumption for population is needed
here.
* Small sample estimation (point estimate and confidence interval
estimate) of population mean when population sigma unknown (will
use sample standard deviation, s, to estimate σ and t tables) – normality
assumption for population is needed here.
*Large sample hypothesis test of population mean when population
sigma known (will use known σ and z tables) – normality assumption for
population not normally needed here.
* Large sample hypothesis test of population mean when population
sigma unknown (will use sample standard deviation, s, to estimate σ and
z tables) – normality assumption for population not normally needed here.
*Small sample hypothesis test of population mean when population
sigma known (will use known σ and z tables) – normality assumption for
population is needed here.
* Small sample hypothesis test of population mean when population
sigma unknown (will use sample standard deviation, s, to estimate σ and t
tables) – normality assumption for population is needed here.
*Large sample estimation (point estimate and confidence interval
estimate) of population proportion (will use sample proportion and z
tables) – large sample sizes need to be verified to use z tables.
* Small sample estimation (point estimate and confidence interval
estimate) of population proportion – cannot work in this course but can
be done with a different statistical structure.
* Large sample hypothesis test of population proportion (will use
sample proportion and z tables) – large sample sizes need to be verified to
use z tables.
* Small sample hypothesis test of population proportion – cannot work
in this course but can be done with a different statistical structure.
*Difference in means problems (similar to those above but you have
different formulas and you will also need to know whether or not the
“two” population standard deviations are equal or unequal)
*Difference in proportions problems (similar to those above but you
have different formulas for each scenario)