AP Statistics Exam Review Flashcards
1
Q
What graphs are appropriate for quantitative data?
A
dotplot, histogram, stemplot, boxplot
2
Q
What graphs are appropriate for categorical data?
A
bar graph, pie graph (not in AP curriculum), 2-way table (I know–it’s not a graph)
3
Q
When creating a graph by hand, always include these:
A
- labels for both axes.
2. numerical scales, with equal intervals labeled, on BOTH axes.
4
Q
What is the difference between marginal and conditional distributions?
A
Marginal distributions are made from numbers in the MARGINS. Conditional distributions are from single rows or columns that are NOT in the margins.
5
Q
When describing (or comparing) distributions, ALWAYS address:
A
shape, center, spread and outliers (SOCS)
6
Q
What can usually be determined from a boxplot?
A
range, IQR, quartiles, MEDIAN
7
Q
What can NOT be determined from a boxplot?
A
shape (at least not a complete description) and sample size
8
Q
When writing COMPARISON statements, always be sure to
A
use COMPARATIVE language (“larger than…”, “both have…”, “more skewed than…,” “neither shows…,” etc.)
9
Q
Stem plots require this for full credit:
A
A key. (Example: 4|3 = 43).
10
Q
Features of a histogram:
A
equal bar (bin) widths, x-axis is a continuous number line, different bin widths may show different features of a distribution, Xscl in TI Window will change bin widths
11
Q
When to use Mean vs. Median?
A
Generally use means with non-skewed data. Use medians with skewed data or data with outliers.
12
Q
When is the mean higher than the median?
A
Generally, this happens when the data is skewed right, or has high outliers.
13
Q
How can you estimate mean and median from a distribution?
A
The mean is the “balance point” if the distribution was made out of a solid material. The median is the “equal areas” location in a distribution.
14
Q
What is standard deviation?
A
It is the “typical” (or average) deviation from the mean in a dataset.
15
Q
When should IQR be used as a measure of spread instead of standard deviation?
A
IQR should be used when the data is skewed or has outliers. Standard deviation should be used when the data is roughly symmetric with no outliers.
16
Q
What is the rule for determining outliers?
A
An outlier is more than 1.5 IQR’s away from the nearest quartile.
17
Q
What is the percentile of x?
A
The percentage of the data that is less than x in a distribution (“less than or equal” is also acceptable).
18
Q
What is “frequency” vs. “relative frequency?”
A
Frequency is counts (whole numbers). Relative frequency is percentage.
19
Q
What is a standardized score?
A
The number of standard deviations from the mean.
20
Q
How do you calculate a z-score?
A
z = (x – mean) ÷ (standard deviation)
21
Q
What statistics/measurements change when you multiply a dataset by a constant?
A
All statistics/measurements change by this same factor (or divisor).
22
Q
What statistics/measurements change by adding (or subtracting) a constant to all data?
A
Only measures of location change. Measures of spread are not affected.
23
Q
What does a density curve show?
A
Overall patterns of a distribution are depicted. Also, the area under the curve is 1 (100%), so percentiles can also be depicted.
24
Q
N(34, 4.2) means
A
a normal distribution with mean 34 and standard deviation 4.2
25
If a dataset has a mean of 34 inches, what will be the units of the standard deviation?
inches
26
What is the difference between a normal density curve and normal data?
The normal density curve will be perfectly normal and symmetric. Data will NEVER be perfectly normal, only APPROXIMATELY normal.
27
The three famous area "rules of thumb" for a normal density curve:
68% of the area is within 1 SD of the mean, 95% of the area is within 2 SD's of the mean, and 99.7% of the area is within 3 SD's of the mean.
28
When reading a z-table, you find that a z-score of 0.62 has a table value of 0.7324. What does this mean?
73.25% of the area under a normal model lies below 0.62 standard deviations above the mean.
29
normalcdf vs invNorm on a TI calculator
normalcdf can find area/percents under a normal model. infNorm can find a z-score given the area to the left (in decimal form)
30
When calculating answers using a Normal model, be sure to communicate:
The type of model you are using (Normal), the parameters (mean, SD), direction of shading, sufficient calculations, the answer in context.
31
What are the general names of the variables on a scatterplot?
x-axis: explanatory variable
| y-axis: response variable
32
What should always be included in a description of a scatterplot?
direction, strength, form, outliers, CONTEXT
33
When should correlation be used and what does it measure?
Correlation should ONLY be used on linear data. It is a measurement of strength and direction of the association between two quantitative variables.
34
When stating the LSRL, include these:
1. "predicted" (put a hat over the y-variable)
2. correct slope and y-intercept values
3. context
35
A LSRL was computed for value ($) and miles driven of a certain make of car. Interpret a slope of -0.134
For every additional 100 miles driven, the value of this car is estimated to decrease by $13.40, according to the LSRL.
36
What's the difference between interpolation and extrapolation?
Interpolation is making a prediction within the range of the data. Extrapolation is making a prediction outside the range of the data.
37
What is a residual?
observed value – predicted value
| Points above the LSRL have positive residuals; points below have negative residuals.
38
What is the best way to justify that a linear model is APPROPRIATE for a scatterplot?
Look at the residual plot. If there is random scatter (no overall curve pattern), then a linear model is appropriate.
39
How can you tell if a linear association is STRONG or not?
1. Look a how close the dots are to the LSRL. The closer they are, the more linear the relationship. 2. Look at r (correlation). Generally between 0.8 and 1 is strong.
40
How can you tell how well a LSRL model FITS the data?
Look at s (standard deviation of the residuals) and r-squared. Lower s's and higher r^2's would generally mean a better fit.
41
What is r-squared?
The percent of variation in the response variable that is accounted for by the LSRL on the explanatory variable.
42
Outliers in the x-direction in a scatterplot:
typically influence the LSRL and the correlation.
43
A strong association in a scatterplot does not automatically imply
a cause-and-effect relationship.
44
How are the terms population, parameter, sample and statistic related?
The population is the entire group of interest. A parameter is a measurement from a population. A sample is a subset of a population; a measure from a sample is a statistic.
45
What is bias?
SYSTEMATIC error in a sample (typically an overestimate or an underestimate)
46
People who choose to be in a sample:
voluntary response sample
47
Generally the best way to get a representative sample:
random sample
48
What makes a simple random sample (SRS) of size n unique?
It guarantees that every SUBSET of size n from the population has an equal chance of being selected.
49
If we want to pick three different students from a group of 10 students, and we use a calculator's random integer function, what instructions are necessary?
1. Number students from 1-10.
2. Do RandInt(1, 10) on a calculator.
3. IGNORING REPEATED NUMBERS, select three students.
50
What is stratified sampling?
Putting subjects into homogenous groups and then selecting a SRS of 20 from each group is called:
51
What is cluster sampling?
Putting subjects into heterogenous groups and then randomly selecting several of these groups for your sample.
52
What does a random sample help guarantee?
1. We can generalize findings to the population.
2. We avoid bias (systematic error in the results)
3. We can invoke probability laws and draw conclusions.
53
What is undercoverage?
When some members of the population are not chosen in a sample.
54
What is nonresponse?
When a chosen individual in a sample does not or chooses not to respond.
55
Observational study vs. experiment
In an experiment, treatments are imposed on subjects and measurements are taken. In an observational study, subjects are only observed and measured.
56
What is confounding?
This occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
57
Factors, levels and treatments in an experiment about 3 dosages of fertilizer on tomato plants and two dosages of water.
Two factors: fertilizer and water
Three levels of fertilizer and two levels of water
Six treatments in all (all six combinations of fertilizer, H2O.
58
Sixteen tanks, each with 20 fish, are set up for a fish food experiment. Four types of fish food are randomly given to 5 tanks each. What are the experimental units?
The 16 tanks. The treatments were assigned to the tanks, not to the individual fish.
59
Describe how you would randomly assign 300 cats to three treatment groups.
One of many correct ways: assign each cat a number 1-300. Put slips of paper with #s 1-300 in a large box and shake well. The 1st 100 #'s picked will be given treatment 1, the 2nd 100 #s will be treatment 2, and the rest will be treatment 3.
60
What are the principles of good experimental design?
Random assignment, control, replication, comparison (and sometimes blocking)
61
What is a double-blind experiment?
When neither the subjects nor those who measure the subject know which treatment was assigned.
62
What is statistically significant?
A result that is not likely to be due to random chance.
63
Can cause and effect be suggested from an experiment?
In a well-designed, completely randomized experiment: YES (but not from only an observational study).
64
What inferences can be drawn from random samples?
Inferences from random samples can be generalized to the population.
65
What inference can be drawn from a completely randomized experiment?
Causation can be inferred from a completely randomized experiment, but only to those subjects (unless those subjects were randomly selected from a population).
66
The Law of Large Numbers:
The proportion of times an event occurs approaches a single value over a LARGE number of observations.
67
The (false) Law of Averages
the incorrect belief that an event's probability must "correct itself" in the short run
68
The probability of an event must be in this range:
0 – 1.
| So if your calculator calculates a probability of 1.2449E–4, remember it's actually 0.00012449
69
Describe how to simulate choosing an SRS of n=5 people from a population of 1200 using a random digit table.
Number each person from 1 to 1200. Then examine four-digit groups of digits in the range 0001–1200. The first five 4-digit numbers, excluding repeats, will be the SRS.
70
If a fair coin was flipped and came up "heads" six times in a row, then is the 7th flip more likely to be "heads" or "tails?"
Neither. Heads and tails are still equally likely. A coin does not have to "correct itself" in the short run. Over a VERY LONG series of flips, a fair coin will approach 50% "heads."
71
When making a conclusion based on data, simulations or a statistical analysis, you could lose credit for saying this:
"proves...," "definitely true...," etc. It is more correct to say "there is convincing evidence...," or "there is not convincing evidence..."
72
What is a probability model?
A depiction of a chance process, including the sample space and probabilities of outcomes. Many times, this is a simple two-row table.
73
When rolling two dice to find the sum, describe an event and an outcome.
An event could be "sum of nine." An outcome could be "rolling a 5 and a 4."
74
If P(A) = 0.42, then the P(complement of A) =
0.58. (Remember: events have complements, not probabilities.)
75
What are mutually exclusive events?
Events that do not have any outcomes in common (also called disjoint events). For example: "picking a heart" and "picking a black card" from a standard card deck.
76
P(jack | red) from a standard card deck =
2/26 = 0.077 (Be sure to show work, even if it is only one calculation.)
77
P(A or B) =
P(A) + P(B) – P(A and B)
| This formula is on the formula sheet.
78
P(A and B) =
P(A) • P(B | A)
| This formula is on the formula sheet, but it's disguised as the conditional formula.
79
Independent events
The occurrence of one event does not affect the PROBABILITY of the other event.
80
Mean (expected value) and standard deviation of a random variable, given a probability table.
These formulas are provided on the formula sheet. REMEMBER: expected valued should NOT be rounded to one of the values in the table! And be sure to show work!
81
Given two independent random variables, X and Y, what is E(X + Y)?
E(X + Y) = E(X) + E(Y)
82
Given two independent random variables, X and Y, what is SD(X – Y)?
The square root of (VAR(X) + VAR(Y)). (It's the VARIANCES that add, not the standard deviations.)
83
What are the characteristics of a binomial probability setting?
B: only two outcomes, "success" and "failure".
I: independent trials. N: number of trials is known in advance. S: same probability of "success" in each trial.
84
What is the binomial formula for calculating probabilities?
The binomial formula is on the formula sheet. The key is to RECOGNIZE a binomial setting when it appears on the exam!
85
What work is required when calculating a binomial probability?
Model used, number of trials (n), value out of n trials (x), probability of a "success." So binompdf(12, 0.34, 4) is OK as long as you clearly define each number.
86
Mean and standard deviation of a binomial probability setting.
These formulas are on the formula sheet--be familiar with them and know how to use them!
87
To win in a dice game, you must roll a 5 or 6. What is the probability that you don't get a 5 or 6 until your fourth roll?
2/3 • 2/3 • 2/3 • 1/3 = 0.099 (failure and failure and failure and success, in that order)
88
What is a SAMPLING distribution?
A distribution of all possible values of a statistic taken from all possible samples of size n.
89
What is an unbiased estimator?
A statistic is unbiased if the mean of its sampling distribution is equal to the parameter it is estimating.
90
What is the difference between a sample distribution, sampling distribution and population distribution?
Population: the distribution from which a sample is taken.
Sample: the distribution of a single sample.
Sampling: the distribution of ALL possible values of a statistic from ALL possible samples of size n.
91
The mean and standard deviation of the sampling distribution of p-hat.
p and √p(1-p)/n
| formula is on the formula sheet
92
The mean and standard deviation of the sampling distribution of x-bar.
µ and σ/√n
| formula is on the formula sheet
93
If the standard deviation of a population is known to be 3.6 inches, what is the standard deviation of a sampling distribution when n = 16?
0.9 inches (3.6 ÷ √16)
94
The central idea of the Central Limit Theorem:
When n is large, the sampling distribution of the sample mean is approximately normal (for ANY population).
95
What does a confidence interval do?
It give a range of plausible values of a population parameter.
96
General formula for a confidence interval:
statistic ± critical value • SD of statistic
| formula is on the formula sheet
97
What is the margin of error?
1. critical value • SD of statistic
| 2. how close we believe our statistic is from the parameter, based on the sampling variability in repeated samples.
98
Explain what 95% confidence means.
In repeated sampling (same n), we expect about 95% of our confidence intervals to capture the true parameter.
99
What is the "template" for interpreting a particular confidence interval?
"I am ___% confident that the true _______ is between ___ and ___."
100
What is the difference between interpreting a confidence INTERVAL vs. a confidence LEVEL?
Interval: a statement of your confidence that the parameter is between two specific numbers.
Level: a general statement about the overall success (capture) rate of your methodology.
101
What word should generally NEVER be used in a confidence interval/level interpretation?
It is very difficult to use the word "probability" correctly when interpreting confidence intervals/levels. Once the interval is created, the true parameter is either captured or not--there is no "probability" after the interval is created.
102
Where could confounding occur in a well-designed, completely randomized experiment?
Confounding is prevented in an experiment by the random assignment of treatments. (Confounding frequently occurs in observational studies, however.)
103
In a 95% confidence interval, what are you fairly sure that the interval contains?
The PARAMETER that you are trying to estimate.
| The statistic MUST be in the interval--in the center!
104
The margin of error of this interval: (15, 25)
5. (The MOE is half of the length of the confidence interval.)
105
Find what's wrong with this statement: "We are 95% confident that the percent of people who said they will vote for Trump is between 45% and 55%."
Using past tense ("said") references the SAMPLE, not the PARAMETER. A confidence interval is an estimate of a PARAMETER. (You are 100% confident you know what people "SAID.")
106
Does increasing sample size produce higher confidence, higher precision, both or neither?
Increasing the sample size will make intervals more precise (shorter). But the "capture rate" will not change, thus the confidence level does not change.
107
What is "standard error?"
When the standard deviation of a statistic is estimated by using p-hat and s instead of using population parameters p and σ.
108
Conditions for 1-proportion z-interval:
Random sample, n 10.
109
Four steps in constructing a confidence interval:
State parameter of interest, check conditions, name the procedure, construct and interpret the interval.
110
Conditions for 1-sample t-interval:
Random sample, n
111
The difference between the null and alternative hypotheses:
Null: "no difference," "no change," etc.
Alternative: the change or difference "hoped/looking for"
112
The null and alternative hypotheses should be all about these:
The POPULATION PARAMETERS (not the sample statistics).
113
One-sided vs. two sided tests
One sided: alternative hypothesis uses .
| Two sided: alternative hypothesis uses ≠.
114
What is a p-value?
The probability that the statistic would be this extreme or more extreme, if the null hypothesis is true.
115
How do you make a decision with the p-value?
If the p-value is alpha, we do NOT reject Ho.
116
What is a Type I error?
The probability of rejecting a true Ho.
117
What is a Type II error?
The probability of NOT rejecting a false Ho.
118
What is power?
The probability that a false Ho is (correctly) rejected.
119
How can power be increased?
Increase sample size or increase alpha. (Or increase the effect size, but that is typically controlled by non-statisticians.)
120
Conditions for 1-proportion z-test:
Random sample, n 10.
121
Test statistic formula:
(statistic – parameter) ÷ SD of statistic
122
Four general steps in a hypothesis test:
Hypotheses, Conditions/Name of test, Work/Calculations, Conclusion
123
Conditions for 1-sample t-test:
Random sample, n
124
How do you calculate the sample size needed for a particular confidence interval?
Set up an inequality using the acceptable margin of error. Solve for n algebraically, then ALWAYS ROUND UP to the next whole number.
125
Conditions for a 2-proportion z-interval:
Two random samples or randomized treatment groups.
| n1 AND n2
126
What work is necessary for two-proportion and two-sample tests and intervals?
Generally, recent exam rubrics require only the test statistic and p-value (for tests) or the correct confidence interval boundaries (for intervals). Any work shown must be consistent with the answer.
127
Conditions for a 2-proportion z-test:
Two random samples or randomized treatment groups.
| n1 AND n2
128
When we fail to reject Ho, this does NOT mean that:
Failing to reject Ho is NOT the same as believing Ho is true. NEVER accept Ho or say anything that communicates that you think Ho is true.
129
Conditions for a 2-sample tests and intervals:
Two random samples or randomized treatment groups.
| n1 AND n2
130
How do you calculate degrees of freedom for t procedures?
For one-sample t: df = (n – 1)
| For two sample t's: use calculator's exact value or the smaller df of either sample, (n1 – 1) or (n2 – 1).
131
How can you tell when you should use a 2-sample t-test vs. a one sample t-test on the paired differences?
Look at how the data was collected. It should be clear whether there are two independent groups or one group in which subjects were "paired" in some way.
132
Which Chi-Square test is used to compare the distributions of counts from 2 or more groups?
Chi-Square Test of Homogeneity
133
Which Chi-Square test is used to compare one distribution to some claim or standard distribution?
Chi-Square Goodness of Fit Test
134
Which Chi-Square test is used to test the independence of two variables within one group?
Chi-Square Test of Independence
135
How do you calculate the Chi-Square statistic?
SUM of [(observed – expected)^2 ÷ expected]
136
Conditions for Chi-Square tests:
Random sample(s) or randomized experiment.
All EXPECTED counts ≥ 5
When sampling: n
137
Degrees of freedom for Chi-Square tests:
GoF: number of categories – 1
| Homog/Ind: (#rows – 1)(#columns – 1)
138
What two things should you do with expected counts?
1. Never round expected counts--they should be reported with a few decimals of accuracy.
2. Always write them down when you check conditions.
139
What is the difference between Chi-Square tests of homogeneity and independence?
Find out how the data was collected. If it was ONE sample "sorted" into two variables, then use independence. If there are two or more independent groups, then use homogeneity.
140
What is the mean of the sampling distribution of b, the slope of the LSRL?
The true slope, β, of the LSRL on the entire population of two-variable data.
141
How do you find the SEb (standard error of the slope) in a linear regression analysis?
Usually, the standard error of the slope is found in a computer-generated table, in the "slope" row under SE.
142
What is the formula for the confidence interval for the true slope, β?
b ± t* • SEb, where t* has (n – 2) degrees of freedom, and SEb is the standard error of the slope.
143
What is one way to calculate SEb if it's not given?
Since the t-statistic = (b – β) ÷ SEb, you could find SEb if you were given t, b and β. (Typically, β is hypothesized to = 0.)
144
What are the conditions for linear regression t-procedures?
Linear data, Independent observations, Normal y's for each x, Equal variance, Random sample/experiment. (LINER)
145
What is the difference between a t* critical value and a t value in a regression table?
t* critical values are used when building confidence intervals, and are found on a t-table using correct confidence level. A t value is how many standard errors the sample slope (b) is from zero.
146
Interpret this 95% confidence interval for the slope of the LSRL comparing arm span and height (cm): (0.50, 0.80)
I am 95% confident that for every additional cm in armspan, the predicted height will increase by between 0.50 and 0.80 cm.
147
If a log transformation on a dataset produces a scatterplot that is linear, then what must be true of the original data?
The original data must be curved if a log transformation straightened it out.
148
In general, if you calculate a numerical answer on the AP Exam, you should also do this:
Always show work for any numerical calculation.
149
In general, if you write TWO different answers or explanations, how will it be graded?
If two parallel answers are given, the "worst" answer will earn the score for that problem.
150
If log(weight) = 3.05(log (length)) – 1.9, then calculate the weight of a fish with length 14.
39.4
