SOPHIA STATISTICS UNIT 2 MILESTONE EXAM
SCRIPT 2026 FULL SOLUTION PRACTICE
◉ Analysis of Variance (ANOVA). Answer: A hypothesis test that
allows us to compare three or more population means.
◉ F statistic. Answer: The test statistic in an ANOVA test. It is the
ratio of the variability between the samples to the variability within
each sample. If the null hypothesis is true, the F statistic will
probably be small.
◉ one-way ANOVA. Answer: A hypothesis test that compares three
or more population means with respect to a single characteristic or
factor.
◉ two-way ANOVA. Answer: A hypothesis test that compares three
or more population means with respect to multiple characteristics
or factors.
◉ chi-square statistic. Answer: Take the observed values.
Subtract the expected values.
Square that difference.
Divide by the expected values.
,Add up all of those fractions.
The sum of the ratios of the squared differences between the
expected and observed counts to the expected counts.
◉ observed frequencies. Answer: The number of occurrences that
were observed within each of the categories in a qualitative
distribution.
◉ expected frequencies. Answer: The number of occurrences we
would have expected within each of the categories in a qualitative
distribution if the null hypothesis were true.
◉ chi-square test for goodness-of-fit. Answer: Step 1: State the null
and alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value.
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
A hypothesis test where we test whether or not our sample
distribution of frequencies across categories fits with hypothesized
probabilities for each category.
,◉ chi-square test of homogeneity. Answer: Step 1: State the null and
alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value.
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ chi-square test for association. Answer: Step 1: State the null and
alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ scatterplot. Answer: A graphical display that allows us to see the
relationship between two quantitative variables.
◉ multiple data sets. Answer: Plotting more than one data set on a
scatterplot requires that we use different colors or symbols for the
different data sets so we can see the relationships separately.
, ◉ form. Answer: The overall shape of the data points. The form may
be linear or nonlinear, or there may not be any form at all to the
points if they form a "cloud."
◉ direction. Answer: The way one variable responds to an increase
in the other. With a negative association, an increase in one variable
is associated with a decrease in the other, whereas with a positive
association, an increase in one variable is associated with an
increase in the other.
◉ strength. Answer: The closeness of the points to the indicated
form. Points that are strongly linear will all fall on or near a straight
line.
◉ explanatory variable. Answer: The variable whose increase or
decrease we believe helps explain a tendency to increase or decrease
in some other variable.
◉ response variable. Answer: The variable that tends to increase or
decrease due to an increase or decrease in the explanatory variable.
◉ correlation. Answer: The strength and direction of a linear
association between two quantitative variables.
SCRIPT 2026 FULL SOLUTION PRACTICE
◉ Analysis of Variance (ANOVA). Answer: A hypothesis test that
allows us to compare three or more population means.
◉ F statistic. Answer: The test statistic in an ANOVA test. It is the
ratio of the variability between the samples to the variability within
each sample. If the null hypothesis is true, the F statistic will
probably be small.
◉ one-way ANOVA. Answer: A hypothesis test that compares three
or more population means with respect to a single characteristic or
factor.
◉ two-way ANOVA. Answer: A hypothesis test that compares three
or more population means with respect to multiple characteristics
or factors.
◉ chi-square statistic. Answer: Take the observed values.
Subtract the expected values.
Square that difference.
Divide by the expected values.
,Add up all of those fractions.
The sum of the ratios of the squared differences between the
expected and observed counts to the expected counts.
◉ observed frequencies. Answer: The number of occurrences that
were observed within each of the categories in a qualitative
distribution.
◉ expected frequencies. Answer: The number of occurrences we
would have expected within each of the categories in a qualitative
distribution if the null hypothesis were true.
◉ chi-square test for goodness-of-fit. Answer: Step 1: State the null
and alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value.
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
A hypothesis test where we test whether or not our sample
distribution of frequencies across categories fits with hypothesized
probabilities for each category.
,◉ chi-square test of homogeneity. Answer: Step 1: State the null and
alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value.
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ chi-square test for association. Answer: Step 1: State the null and
alternative hypotheses.
Step 2: Check the conditions.
Step 3: Calculate the test-statistic and p-value
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ scatterplot. Answer: A graphical display that allows us to see the
relationship between two quantitative variables.
◉ multiple data sets. Answer: Plotting more than one data set on a
scatterplot requires that we use different colors or symbols for the
different data sets so we can see the relationships separately.
, ◉ form. Answer: The overall shape of the data points. The form may
be linear or nonlinear, or there may not be any form at all to the
points if they form a "cloud."
◉ direction. Answer: The way one variable responds to an increase
in the other. With a negative association, an increase in one variable
is associated with a decrease in the other, whereas with a positive
association, an increase in one variable is associated with an
increase in the other.
◉ strength. Answer: The closeness of the points to the indicated
form. Points that are strongly linear will all fall on or near a straight
line.
◉ explanatory variable. Answer: The variable whose increase or
decrease we believe helps explain a tendency to increase or decrease
in some other variable.
◉ response variable. Answer: The variable that tends to increase or
decrease due to an increase or decrease in the explanatory variable.
◉ correlation. Answer: The strength and direction of a linear
association between two quantitative variables.
