Statistics Lab Worksheet

PPOL 552-01 Research Methods

PART 2. Let’s use
the sample data to make some confidence interval estimates:

Example A:

** estimate
a 95% confidence interval for mean age

ci means age, level (95)

<COPY
AND PASTE STATA COMMAND AND OUTPUT HERE>

Example A Interpretation:

·
Based on this sample, I am ___95___% confident that the population
mean age is between _______52.3____years_____
and ________54.7
years________ .

·
Being _95_____% confident” means that _95__% of the possible samples would produce
confidence intervals that contain the actual population mean. It also means
that, due to sampling error, there is a ____5__% chance
of drawing a sample and estimating a confidence interval from it that doesn’t
contain the population mean.

Example B
Interpretation:

** estimate
99% confidence interval for a categorical variable’s proportions

proportion educ,
level(99)

<COPY
AND PASTE STATA COMMAND AND OUTPUT HERE>

Example B Interpretation:

·
Based on this sample, I am ___99___% confident that
between ___11.2___%
and __16.9____% of
the population has a graduate degree. I am also __99____% confident that
between ___10.8___%
and __16.3____% of
the population has a two-year associate degree.

·
Since these two confidence intervals DO overlap each other, I

CANNOT be
confident about which of these two groups is likely to be the largest in the
population. They could even be exactly equal in size, even though the estimates
are not equal.

·
I am also __99____% confident that a third group, those whose
highest degree is a bachelor’s degree, is larger than either of the two groups
discussed above because its confidence interval (__18.0____% to __24.7____%) DOES NOT overlap either of the other two
confidence intervals.

Example C:

** estimate
proportion intervals for values of another categorical variable

proportion educ,
over(ownhome) level(95)

<COPY
AND PASTE STATA COMMAND AND OUTPUT HERE>

Example C Interpretation:

·
Based on this sample, I am __95____% confident that between __15.0____% and ___20.7___% of those who own
a home in the population have graduate degrees.

·
I am also ___95___% confident that between ___3.1___% and ___8.3___% of those who rent in the population
have graduate degrees.

·
Since these two intervals DO NOT overlap, I am also _95_____% confident that
a(n)

EQUAL / LARGER /
SMALLER proportion of home owners have graduate degrees compared to renters.

·
This finding MIGHT suggest that the amount of education and home
ownership have a pattern of association in the population. (Further statistical
testing is needed to assess this possibility, which we will investigate in
Statistics Lab 2).

Example D:

** estimate
proportion intervals for values of another categorical variable

proportion WEED4,
over(mstatus) level(95)

<COPY
AND PASTE STATA COMMAND AND OUTPUT HERE>

Example D Interpretation:

·
Based on this sample, I am ______% confident that
between ______% and ______% of those who are married in the population have smoked
marijuana.

·
I am also ______% confident that between ______% and
______% of those who are divorced in the population have smoked marijuana.

·
Since these two intervals DO / DO NOT
overlap, I am also ______% confident that a(n)

EQUAL / LARGER / SMALLER proportion of married individuals have smoked
marijuana compared to individuals who are divorced.

·
This finding MIGHT / MIGHT NOT suggest that martial
status and using marijuana have a pattern of association in the population. (Further
statistical testing is needed to assess this possibility, which we will
investigate in Statistics Lab 2).

PART 3. Prepare
some inferences of your own using the commands above.

For Part 3 of the worksheet, investigate these data further using the
summary statistics commands. Your goal should be to develop three new and
interesting findings about the population of American adults (so you may not
use the example findings in this document). You may use any of the statistical
procedures we learned as shown in step 2 above, but your findings must include
at least two confidence interval estimates.

In writing up your results, you should include the Stata command you ran
and its results, clearly highlighting the relevant information in those
results. Then describe the results concisely, and provide a clear
interpretation of the results in plain language. You should consult the
examples we completed in class in Part 2, but must write your results in your
own words. Be sure to focus on what you’ve learned about the POPULATION, not
the sample—remember, that is the goal of statistical inference.

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