chapter 8 Flashcards
what is an interval estimate
often computed by addition and subtracting a value
what is z a/2
critical value
if you have a high critical value then your margin of error will be
high
What is the purpose of an interval estimate
provides info about how close the point estimate is to the value of the pop parameter
What is the purpose of an interval estimate
provides info about how close the point estimate is to the value of the pop parameter
HOw do you calculate the margin of error with Q known
z a/2 x SE
If you have a 95% confidence what is your critical value and z-score
critical value is 1-.95 = 0.05
z a/2 = 0.05/2 = 0.025
z= -1.96
How do you calculate the interval when you know Q
x bar +- za/2 x SE (q / square root of n)
What is the confidence coefficent for a 95% confidence level
1 -.95 = 0.05
a = 0.05
What are the most commonly used Confidence Levels
- 90%
- 95%
- 99%
What are the most commonly used Confidence levels and their corresponding critical values and z scores
- 90% cv = .10 z = 1.645
- 95% CV = .05 z = 1.96
- 99% CV = .01 z = 2.576
In order to have a higher degree of confidence, the margin of error
and width of the interval must be larger
If the population does NOT follow a normal distribution for confidence intervals
- the confidence interval will be appromate
- quality of the approx. depends on
- distribution of the pop
- sample size
most applications, sample size of 30 or more is adequate
IF the population is not normally distributed but it is roughly symmetrical what sample size can produce a good approx confidence interval
n = 15 can be expected to provide a good aprpox. confidence interval
What if you have smaller sample sizes than 15
should only be used if the analyst believes pop distribution is at least approx. normal
How do you calculate an interval estimate if you don’t know Q
use t-distribution and df (n-1)
at what level of df does the t-distribution become the standard normal distribution
more than 100 degrees of freedom
As the number of df gets higher, what happens
the difference b/w the t-distribution and the normal distribution (z-table) becomes smaller and smaller
- it becomes less variable and more closely resembles the standard normal distribution
what is the mean of the t-distribution
0
what it the formula for the interval for x bar when Q is not known
x bar +- s / (square root of n)
how do you calcualte the standard error when you don’t know Q`
s = square root of (sum (x-x bar) squared / n-1
When the pop does NOT follow normal distriubiton, the confidence interval will
be aprox
- the quality of the approx depends on
- distribution of the pop
- sample size
most applcations what sample size is sufficent when Q is not known what should the sample size be at least
n is greater than or equal to 30
what if the distribution is highly skewed or has outliers what should the minimum sample size be
sample size of 50 or more
what if the distribution is roughly symmetrical what sample size should work
15 or more
WHen determining the sample size needed for a desired margin of error how can you compute the planning value of Q
- use the estimate of the pop sd computed from the data of previous studies as a Planning value of Q
- use a pilot study to select a preliminary sample. the sample SD form this can be used as the planning values for Q
- use judgement for the values of Q
ex. we might begin by estimating the largest and smallest data values in the pop
largest - smallest -> gives us an estimate for the range of data.
range / 4 = often suggested for a rough approx of the SD and thus acceptable planning value of Q
What is the formula for the interval estimate for a Pop Proportion
p hat +- z a/2 (p hat +- square root p(1-P)/n)
In practice how do you determine the sample size for Proportion (different ways)
- use the sample proportion from a previous sample of the same or similar units
- use a pilot study to select a preliminary sample
- the sample proportion from this can be used as the planning value of P* - use judgement or best guess p*
- if none of the proceeding alternatives apply, use planning value of p* =.50
explain p*=.50 (planning value)
the largest value of P(1-P) occurs when P* = .50
- this provides the largest sample size
- this plays it safe
- if sample size turns out to be different than .50, margin of error will be smaller than anticipated
- thus, .50 will be sufficient to obtain the Margin of Error
what is the desired margin of error for pop proportion
.10 or less
what is also a common margin of error for pop proprotion other than .10
.03 or .04 margin of error is common
in interval estimation, when the sample size becomes larger, the interval estimate
becomes narrower
The absolute value of the difference between the point estimate and the pop parameter it estimates is the
sampling error
as the number of df for a t distribution increases, the difference bw the t distribution and the standard normal distribution becomes
becomes smaller
In an interval estimation, the t distribution is used only when the
sample standard deviation is used to estimate the pop standard deviation
The ability of an interval estimate to contain the vlaue of the pop parameter is described by the
confidence level
in general, higher confidence levels provide
wider confidence intervals
an interval estimate is a range of values used to estimate
a population parameter
when the level of confidence decreases, the margin of error
becomes smaller
