College in High School Statistics 200
Data Analysis/Statistical Inference Problems Using Class Survey Data
Use any of the data provided in the compiled responses to the class
survey. Be sure to begin each problem with an opening statement, telling what
you intend to do. Tell what you anticipate the outcome of your analysis will
be. (If you really can't make a guess, just say so.) Finish with a
concluding statement which summarizes your findings.
Remember, the TEACHER gives the STUDENT the assignment, not the other way around! If you
use MINITAB, all
output must be explained by YOU in order to receive credit.
- Thoroughly describe and display a quantitative data set. Be
sure to mention center, spread, shape, and possibly outliers; include
dotplot, stemplot, boxplot, and histogram.
- Compare values of a quantitative variable for 2 or more groups. Be
sure to compare centers, spreads, and shapes; include side-by-side boxplots.
- Examine the relationship between 2 quantitative variables. Include
a scatterplot, mention of direction, form, and strength; correlation and
the regression line equation if the relationship appears linear; mention
of outliers or influential observations if present.
- Examine the relationship between 2 categorical variables. Display
the data with a two-way table. Summarize the
relationship by comparing relative frequencies.
Note: for the statistical inference problems, we will assume our class
to be a random sample of Pitt students. This may or may not be a
reasonable assumption, depending on the variables studied. Unless you
happen to know population standard deviation (eg. for heights or
weights), you will need to work with sample standard deviation. This
will affect your choice of a z or t procedure. Examine
plots of the data to decide if the Central Limit Theorem applies for the
given sample size.
- Set up a confidence interval for the mean of a quantitative variable.
- Test a hypothesis about the mean of a quantitative variable.
- Set up a confidence interval for the difference between means for 2
groups. (Look at sample standard deviations to decide whether or not to
use a pooled procedure.)
- Test if the difference between means for 2 groups is zero. (Decide
whether or not to use a pooled procedure, and make sure you formulate a
reasonable alternative hypothesis.)
- Use ANOVA to compare means for more than 2 groups.
- Set up a confidence interval for a proportion based on categorical data.
- Test a hypothesis about a proportion.
- Set up a confidence interval for the difference between proportions
for 2 groups.
- Test if the difference between proportions for 2 groups is zero.
- Use chi square to test for a relationship between 2 categorical variables.
- Examine a relationship between 2 quantitative variables as in #3.
If it appears linear, estimate the regression model parameters and tell
what they mean;
test the null hypothesis that the slope of the regression line is zero.
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