AP Exams

Question 1

Interpret a z-score

Answer 1

A z-score describes how many standard deviations a value or statistic (x, x, P, etc.) falls away from the mean of the distribution and in what direction.
The further the z-score is away from zero the more
“surprising” the value of the statistic is.

Question 2

Describe the Distribution
OR
Compare the Distributions

Answer 2

SOCS!
Shape, Outliers, Center, Spread
Only discuss outliers if there are obviously outliers present. Be sure to address SCS in context!
If it says “Compare”
YOU MUST USE comparison phrases like “is greater than” or “is less than” for Center & Spread

Question 3

Geometric Distribution
(Conditions)

Answer 3

1. Binary? Trials can be classified as success/failure
2. Independent? Trials must be independent.
3. Trials? The goal is to count the number of trials until the first success occurs
4. Success? The probability of success (p) must be the same for each trial.

Question 4

Outlier Rule

Answer 4

Upper Bound = Q3 + 1.5(1QR)
Lower Bound = QI - 1.5(IQR)
IQR = Q3 - li

Question 5

What is a Residual?

Answer 5

Residual = y - y
A residual measures the difference between the actual (observed) y-value in a scatterplot and the y-value that is predicted by the
LSRL using its corresponding x value.
* In the calculator: L3 = L2 - Y,(L1)

Question 6

Inference for Proportions (Conditions)

Answer 6

Random: Data from a random samples) or randomized experiment
Normal: At least 10 successes and failures (in roth groups, for a two sample problem)
Independent: Independent observations and independent samples/groups; 10% condition if sampling without replacement

Question 7

Type I Error, Type II Error,
& Power

Answer 7

1. Type I Error: Rejecting Ho when Ho is actually true. (Ex. Convicting an innocent person
2. Type II Error: Failing to (II) reject Ho when Ho should be rejected. (Ex. Letting a guilty person go free)
3. Power: Probability of rejecting Ho when Ho should be rejected. (Rejecting Correctly)

Question 8

Mean, and Standard
Deviation Of a
Binomial Random Variable

Answer 8

Also on the formula sheet!
Mean: μx = np
Standard Deviation:
σx = пp(I-p)

Question 9

Inference for Regression (Conditions)

Answer 9

Linear: True relationship between the variables is linear.
Independent observations, 10% condition if sampling without replacement
Normal- Responses vary normally around the regres.
line for all x-values
Equat var ‘ance around the regression line for all x-values
Landom: Data from a random sample or randomized
experiment

Question 10

Mean and Standard
Deviation of a
Discrete Random Variable

Answer 10

Also on the
formula
Mean (Expected Value):
sheetl
M. = [x,P.
(Multiply & add across the table)
Standard Deviation:
0, = VI(x, - M.) P.
Square root of the sum of (Each x value - the mean) (its probability)

Question 11

Inference for Means (Conditions)

Answer 11

Random: Data from a random samples) or randomized experiment
Normal: Population distribution is normal or large samples) (n, ≥ 30 or n, ≥ 30 and n2 ≥ 30)
Independent: Independent observations and independent samples/groups; 10% condition if sampling without replacement

Question 12

Interpreting
Expected Value/Mean

Answer 12

The mean/expected value of a random variable is the long-run average outcome of a random phenomenon carried out a very large number of times.

Question 13

Binomial Distribution
(Conditions)

Answer 13

1. Binary? Trials can be classified as success/failure
2. Independent? Trials must be independent.
3. Number? The number of trials (n) must be fixed in advance
   4: Success? The probability of success (p) must be the same for each trial.

Question 14

Interpret
LSRL y-intercept “a”

Answer 14

When the x variable (context) is zero, the y variable (context) is estimated to be put value here.

Question 15

Using Normal cdf and
Invnorm
(Calculator Tips)

Answer 15

Normalcdf (min, max, mean, standard deviation)
Invnorm (area to the left as a decimal, mean, standard deviation)

Question 16

Interpret r

Answer 16

Correlation measures the strength and direction of the linear relationship between x and y.
• r is always between -1 and 1.
• Close to zero = very weak,
• Close to 1 or -1 = stronger
• Exactly 1 or -1 = perfectly straight line
• Positive r = positive correlation
• Negative r = negative correlation

Question 17

Interpret
LSRL Slope “b”

Answer 17

For every one unit change in the x variable (context)
the y variable (context)
is predicted to increase/decrease by [ ] units (context).

Question 18

Chi-Square Tests
df and Expected Counts

Answer 18

1. Goodness of Fit:
   df = # of categories - 1
   Expected Counts: Sample size times hypothesized proportion in each category.
2. Homogeneity or Association/Independence:
   df = (# of rows - 1)(# of columns - 1)
   Expected Counts: (row total)(column total)
   table total

Question 19

Interpret
Standard Deviation

Answer 19

Standard Deviation measures spread by giving the “typical” or “average” distance that the observations (context) are away from their (context) mean

Question 20

Experimental Designs

Answer 20

1. CRD (Completely Randomized Design) - All experimental units are allocated at random among all treatments
2. RBD (Randomized Block Design) - Experimental units are put into homogeneous blocks.
   The random assignment of the
   units to the treatments is carried out separately within each block.
3. Matched Pairs - A form of blocking in which each subject receives both treatments in a random order or the subjects are matched in pairs as closely as possible and one subject in each pair receives each treatment, determined at random.

Question 21

Complementary Events

Answer 21

Two mutually exclusive events whose union-is the sample space.
A
Ex: Rain/Not Rain,
Draw at least one heart / Draw NO hearts

Question 22

Sampling Techniques

Answer 22

1. SRS- Number the entire population, draw numbers from a hat (every set of n individuals has equal chance of selection)
2. Stratified - Split the population into homogeneous groups, select an SRS from each group.
3. Cluster
   - Split the population into heterogeneous groups called clusters, and randomly select whole clusters for the sample. Ex. Choosing a carton of eggs actually chooses a cluster (group) of 12 eggs.
4. Census - An attempt to reach the entire population
5. Convenience
   Selects individuals easiest to reach
6. Voluntary Response -
   - People choose themselves by
   responding to a general appeal.
   I am from
   % confident that the interval captures the true
   STATE: What parameter do you want to estimate, and
   at what confidence level?
   PLAN: Choose the appropriate inference method.
   Check conditions.
   DO: If the conditions are met, perform calculations.
   CONCLUDE: Interpret your interval in the
   context of the problem.
   Standard Deviation measures spread by giving the “typical” or “average” distance that the observations (context) are away from their (context) mean
7. Is there a curved

Question 23

Interpreting
a Residual Plot

Answer 23

1. Is there a curved pattern? If so, a linear model may not be appropriate.
2. Are the residuals small in size? If so, predictions using the linear model will be fairly precise.
3. Is there increasing (or decreasing) spread? If so, predictions for larger (smaller) values of x will be more variable.

Question 24

Explain a P-value

Answer 24

Assuming that the null is true (context) the P-value measures the chance of observing a statistic (or difference in statistics) (context)
as large as or larger than the one actually observed.

Question 25

Interpreting a Confidence Interval (Not a Confidence Level)

Answer 25

I am [ ] % confident that the interval from [ ] to [ ] captures the true [ ].

Question 26

4-Step Process Confidence Intervals

Answer 26

STATE: What parameter do you want to estimate, and at what confidence level? PLAN: Choose the appropriate inference method. Check conditions. DO: If the conditions are met, perform calculations. CONCLUDE: Interpret your interval in the context of the problem.

Question 27

Finding the Sample Size (For a given margin of error)

Answer 27

For one mean: m= N p(l-p) For one proportion: m If an estimation of p is not given, use 0.5 for p. Solve for n. The data is collected in such a way that there is no systematic tendency to overestimate or underestimate the true value of the population parameter. (The mean of the sampling distribution equals the true value of the parameter being estimated) The systematic favoring of certain outcomes due to flawed sample selection, poor question wording, undercoverage, nonresponse, etc. Bias deals with the center of a sampling distribution being "off"! Yes, if: A large random sample was taken from the same population we hope to draw conclusions about. STATE: What hypotheses do you want to test, and at what significance level? Define any parameters you use. PLAN: Choose the appropriate inference method. Check conditions. DO: If the conditions are met, perform calculations. Compute the test statistic and find the P-value. CONCLUDE:

Question 28

Unbiased Estimator

Answer 28

The data is collected in such a way that there is no systematic tendency to overestimate or underestimate the true value of the population parameter. (The mean of the sampling distribution equals the true value of the parameter being estimated)

Question 29

Bias

Answer 29

The systematic favoring of certain outcomes due to flawed sample selection, poor question wording, undercoverage, nonresponse, etc. Bias deals with the center of a sampling distribution being "off"!

Question 30

Can we generalize the results to the population of interest?

Answer 30

Yes, if: A large random sample was taken from the same population we hope to draw conclusions about.

Question 31

4-Step Process Significance Tests

Answer 31

STATE: What hypotheses do you want to test, and at what significance level? Define any parameters you use. PLAN: Choose the appropriate inference method. Check conditions. DO: If the conditions are met, perform calculations. Compute the test statistic and find the P-value. CONCLUDE: Interpret the result of your test in the context of the problem.