UW-W ECON 245 EXAM 3
predictive interval
A ________ tells you an upper and lower bound such that a certain percentage of observed data values lie within the upper and lower bounds.
sampling, underlying, data points, mean
A confidence interval is not likely to contain a majority of the data points because: 1) Our confidence levels are made from the _________distribution and not the _________ distribution. 2) Many _________ are typically farther away from the _________.
dispersion (o)
All of our confidence intervals can be thought of as having the following form: point estimate +/- some quantity. The "some quantity" depends on our sample size, our desired confidence level, and the level of ________.
two-sided confidence interval
Allowing the confidence to contain points both greater than and less than the point estimate
1.645
Appropriate z-score for a 90% confidence level
1.96
Appropriate z-score for a 95% confidence level
2.575
Appropriate z-score for a 99% confidence level
o, mean
Constructing a confidence interval around x bar where you know o is pretty dumb, because it supposes you know ________ but you don't know ________.
predictive interval
For any normally distributed phenomenon, a majority of the data points will be found within the intervals.
more likely
If we lower the confidence level of a hypothesis test, we are _________ to reject the null hypothesis
less likely
If we raise the confidence level of a hypothesis test, we are _________ to reject the null hypothesis.
two-sided
If we want to allow for the possibility that our point estimate may be both greater than or less than the population parameter we should construct a _________ confidence interval.
critical value
In order to carry out a hypothesis test, you need to know a test statistic and compare it to a ________.
s
In the event that we don't know o, we work with its very reasonable proxy ________.
accuracy, precision
Large confidence levels will give you high _________ but low _________
believe, evidence
One of the problems with the conclusion "fail to reject the null hypothesis" is that we may not really ________ the null hypothesis, it's just that we haven't marshalled enough ________ to reject it.
precision, accuracy
Smaller confidence levels will give higher _________ but lower _________.
squashed, tails, variance
Some things to note about the t-distribution: 1) Looks like a slightly "_________" normal distribution 2) More mass in the _________ and less in the peak 3) Has a higher _________ than a normal distribution
H1
Suppose I meet with the parole board to see if I should be paroled. The parole board decides I am reformed and frees me only to discover months later that I was far from reformed. Then ________ = I am reformed.
a type 2, no
Suppose you decide to drive drunk under the presumption that you won't get caught. A cop notices that you are drifting, suspects you are drunk, and decides to investigate. The end result is that you have to go to jail for aggravated driving while intoxicated. Then: you committed ________ error, the cop committed ________ error
o, large, small
The basic varieties of the confidence interval formula arise from two considerations. They are: 1) Do we know _________? 2) Is the sample _________ or _________?
William Gosset
The discovery of the t-distribution is generally credited to:S
standard error
The quantity by which we scale our z-score
student
The t-distribution is also known as the ________ distribution.
hypothesis testing
Trying to see if a particular claim is valid or not
sample size
We use the t-distribution when our ________ is small.
small sample size
When is it appropriate to use the t-distribution?
increase of sample size
Which of the following implies we need not face the precision vs. accuracy trade-off?
all of the above are true
Which of the following is not true of the t-distribution?
precision, accuracy
With a confidence interval, as you increase the confidence level: you decrease ________, but increase ________
point estimate+/-some quantity
confidence interval
degrees of freedom
n-1
type 2 error
occurs when fail to reject a false null hypothesis
type 1 error
occurs when we reject a true null hypothesis
interval estimation
primarily takes the form of calculating an interval that we believe contains a population parameter on the basis of information in a sample
t.050
t value for 90% confidence level
t.025
t value for 95% confidence level
t.005
t value for 99% confidence level
null hypothesis
the claim being mad and what we are seeking to test, usually written as H0
margin of error
the maximum sampling error permitted (E)
standard error
the standard deviation of the sampling distribution, using the sample standard deviation
statistical inference
the use of sample statistics to infer something about population parameters
alternative hypothesis
when the null hypothesis is false, usually written as H1
type 1
whenever we lower the confidence level, we are increasing the risk of _________ error
type 2
whenever we raise the confidence level, we are increasing the risk of a _________ error.
fail to reject the null hypothesis
z- or t-score < critical value
reject the null hypothesis, accept the alternative
z- or t-score > critical value
