Hypothesis Test correct answers 1) form alternative and state null
2)calculate test stat
3)find rejection region's critical value or p value
4)make decision based on where test statistic falls (within or not within rejection region)
(p value higher than alpha= DNR
p value lower than alpha=R)
...
Econ 203 || with 100% Errorless Solutions.
Hypothesis Test correct answers 1) form alternative and state null
2)calculate test stat
3)find rejection region's critical value or p value
4)make decision based on where test statistic falls (within or not within rejection region)
(p value higher than alpha= DNR
p value lower than alpha=R)
Confidence Interval correct answers 1) point estimate
2) z,t,f value associated with finding upper and lower limits
3) find margin of error
4) upper and lower bounds based on confidence interval percentage
chi-squared o^2 correct answers graph always centered on n-1(also what degrees of freedom
are), non-negative and skewed towards the right, chi squared may be used if interested in the
consistency of a production process for quality control purposes; assessing the "risk" of a
particular investment. chi squared can be identified quickly when there is one single population
variance stated. population variance is usually always found in the null. for ex: "operations
should not exceed 4.0 degrees".
difference in means:case 1 u1-u2 correct answers independent samples from two populations of
data where each sample does not have any affect on the other data, this is where two population
variances are known because they are stated in the question and you can use z distribution. (u1-
u2) and follow z across.
difference is means:case 2 u1-u2 correct answers independent samples from two populations of
data where each sample does not have any affect on the other data, this is where you assume the
unknown population variances are equal because that is what the null states. Use t statistic and
degrees of freedom are n1+n2-2. You must find pooled variance s^2p) before calculating the test
statistic.
comparison of two populations correct answers interested in the difference between two
populations parameters and may ask questions like "Is Econ 203 grade-point higher than that of
202?" or "Does Obama have more support than last month?" "Which of these two stocks is
safer?"
difference in means:case 3 u1-u2 correct answers independent sample from two populations of
data where each sample does not have any affect on the other data, this is where two population
variances are unknown and you assume they are unequal because of the null. Use t statistic for
this and degrees of freedom is long formula diving sample variances from there populations.
**Remember to square the standard deviations to make them variances**
difference in means; dependent sample/matched pairs ud correct answers dependent samples
means that samples were drawn and there is an indentifiable link between sample data 1 from
each population. Usually in a more "controlled" environment. there are fewer outside factors to
, impact results. Use t statistic and degrees of freedom are nd-1. **almost identical to single
population means test**
difference in proportions test; case 1 p1-p2 correct answers two populations whose data is
qualitative= only ask questions regarding the proportions of occurrences of certain outcomes.
case 1 is always equal to 0 for the null. When that happens you must then calculate the pooled
proportion and use that to calculate your z stat. Z always used in proportions because only
talking about populations. "Is the percentage of A's given in colleges and universities this year
higher than that of ten years ago?" or "Is the proportion of democratic voters greater than the
proportion of reupublican voters?" no additional info so assume they equal each other and
therefore null is 0.
difference in proportions; case 2
p1-p2 correct answers two populations whose data is qualitative= only ask questions regarding
the proportions of occurrences of certain outcomes. Case two has a null hypothesis that does not
equal 0. It will be some outside information: "Is the percentage of A's given in colleges and
universities this year is more than 2.5% higher than that of ten years ago?" or "Is the proportion
of democratic voters more than 5% greater than the proportion of reupublican voters?" 2.5 and
5% represent D and make null not equal to 0. When that happens you must calculate individual
sample proportions. You will use Z dist.
when to use Ratio of Two Variances Test correct answers comparing the variability of two
populations but rather than use differences we use the ratio of one over the other to do analysis.
Use sample statistics (sample variances) to draw conclusions about the population parameter. use
this test when: variety of situations where variances are of direct interest. For instance, when
evaluating the consistency of processes or risk of investing; determine which difference in means
test to use when we have independent samples: equal variances test.
case 1 for ratio of two variances tests s1^2, s2^2 correct answers null hypothesis always equal to
one and alternative can be not equal, >,< to 1. Construct and F statistic for this test. key words
could be is "there a difference in the consistency?" because this needs to be in ratio it makes
sense that s1/s2 would be equal to one (as they need to be) because the null is that they are
always unequal. degrees of freedom for this is: n1-1,n2-1.
case 2 for ratio of two variances test o1^2 o2^2 correct answers F test for unknown population
variance is equal or unequal. This is when a difference in means test does not state whether to
assume the unknown population variances are equal or not. Our null is that the population
variances do equal eachother and the alternative is that they do not. We use the sample variances
to find the test statistics and the populations to find the degrees of freedom for the f value. We
use F test because it doesnt require population variances due to the ratio of sample stats. If we
DNR the null that they are equal we continue original problem with the steps used for case 2. if
we do reject the null and accept H1 we use following steps for case 3 on original problem.
F distribution correct answers very similar to chi squared in that it is non negative and positively
skewed. the center of distribution is usually around 1. degrees of freedom are v1=n1-1 for
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