Exam (elaborations)
Stats 151 Final Exam Questions And Answers Latest Update
- Course
- Stat-151
- Institution
- Massachusetts Institute Of Technology
Stats 151 Final Exam Questions And Answers Latest Update
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Solution 2024/2025Pepper
Stats 151 Final Exam Questions And Answers
Latest Update
Special Addition Rule ANS✔✔ P(A or B) = P(A) + P(B)
Special Multiplication Rule ANS✔✔
General Addition Rule ANS✔✔ P(A or B) = P(A) + P(B) - P(A and B)
Complement Rule ANS✔✔ The probability of an event occurring is 1 minus
the probability that it doesn't occur
chi-square goodness of fit test ANS✔✔ Statistical test used to evaluate how
well a set of observed values fit the expected values. The probability
associated with a calculated chi-square value is the probability that the
differences between the observed and the expected values may be due to
chance. A test of whether the distribution of counts in one categorical
variable matches the distribution predicted by a model is called a test of
goodness-of-fit. In a chi-square goodness-of-fit test, the expected counts
come from the predicting model. The test finds a P-value from a chi-square
model with k −1 degrees of freedom, where k is the number of categories of
the categorical variable (and not the sample size) (p. 690).
Cell ANS✔✔ One element of a two-way table corresponding to a specific row
and a specific column. Table cells can hold counts, percentages, or
measurements on other variables, or they can hold several values (p. 692).
Chi-square statistic ANS✔✔ can be used to test whether the observed
counts in a frequency distribution or contingency table match the counts we
, Solution 2024/2025
Pepper
would expect according to some model. It is calculated as: x2 = sum of all
cells (obs - exp) 2 divided by exp. Chi-square statistics differ in how
expected counts and degrees of freedom are found, depending on the
question asked (p. 693).
Chi-square model ANS✔✔ Chi-square models are skewed to the right. They
are parameterized by their degrees of freedom and become less skewed
with increasing degrees of freedom (p.693).
Chi-square component ANS✔✔ The components of a chi-square calculation
are (obs-expected)2 divided by expected found for each cell of the table
(p.696).
Two-way table ANS✔✔ Each cell of a two-way table shows counts of
individuals. One way classifies a sample according to a categorical variable.
The other way can classify different groups of individuals on the same
variable or classify the same individuals according to a different categorical
variable (p.698).
Chi-square test of homogeneity ANS✔✔ A test comparing the distribution of
one categorical variable in two or more groups. A chi-square test of
homogeneity finds expected counts based on the overall frequencies,
adjusted for the totals in each group under the (null hypothesis) assumption
that the distributions are the same for each group. We find a P-value from a
chi-square distribution with (#Rows − 1) × (#Cols − 1) degrees of freedom,
where #Rows gives the number of categories for the categorical response
variable and #Cols gives the number of independent groups (or vice versa)
(p. 699).
Standardized residual ANS✔✔ In each cell of a two-way table, a
standardized residual is the square root of the chi-square component for
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