AP Final Exam

Question 1

SOCS - fairly symmetric

Answer 1

• Shape
• Center- mean
• Spread - SD
• Outliers - too small if Q1 - 1.5
  too big is Q1 + 1.5

Question 2

SOCS - slightly/strongly skewed

Answer 2

• Shape
• Center - median
• Median - IQR
• Outliers - too small if Q1 - 1.5
  too big is Q1 + 1.5

Question 3

How to find SOCS easily

Answer 3

Make list –> stats –> stat calc –> 1 variable stats

Question 4

True or false: you can determine the shape with a boxplot

Answer 4

False

Question 5

Interpret SD

Answer 5

The (context) typically varies by (SD) from the mean of (mean).

Question 6

Interpret percentile

Answer 6

(Percentile) % of (context) are less than or equal to (value).

Question 7

Interpret z-score

Answer 7

(Specific value w/ context) is (z-score) standard deviations (above/below) the mean.

Question 8

Describing the distribution

Answer 8

DUFS:
- Direction - (+) or (-)
- Unusual features - outliers or clusters
- Form - linear or nonlinear
- Strength - weak, moderate, or strong

Question 9

Calculate slope

Answer 9

use b in y(hat) = a + bx –> b/increment (ex. years)

Question 10

Interpret slope

Answer 10

The predicted (y-context) (increases/decreases) by (slope) for each additional (x-context).

Question 11

Interpret coefficient of determination (r^2)

Answer 11

(r^2 as percentage) of the variation in (y-context) can be explained by the linear relationship with (x-context).

Question 12

Calculate residual (r)

Answer 12

r = (actual) - (predicted)
predicted = y(hat) = a + bx

Question 13

Interpret residual (r)

Answer 13

The actual (y-context) was (r) less/greater than the predicted (y-context & predicted value).

Question 14

Convenience sample

Answer 14

Selected for inclusion because they are easy to access
(ex. first 30 people to walk through the door)
- Underestimates or overestimates true proportion
- Not representative of population

Question 15

Voluntary response

Answer 15

Choose to participate in a survey or experiment

Question 16

Simple random sample

Answer 16

Random sample which takes a random population and randomly assigns them into groups with equal probability.

Question 17

Stratified sampling

Answer 17

Takes population and splits them into groups (strata) into a characteristic that we think has some effect.
(ex. SRS within grades)
- Homogeneous groups
- SRS within each group

Question 18

Cluster sample

Answer 18

Grouping is similar to population and SRS is taken to choose a cluster.
(ex. SRS of classrooms)
- Heterogeneous groups
- SRS of groups

Question 19

Undercoverage bias

Answer 19

Don’t have access to survey

Question 20

Response bias

Answer 20

No reply

Question 21

Response bias

Answer 21

Participants who are untruthful

Question 22

Confounding variable

Answer 22

Variable that causes suspicious association

Question 23

Observational study

Answer 23

Variables are observed to determine if there’s a correlation

Question 24

Experimental study

Answer 24

Using controlled variables to determine if there’s causation

Question 25

Use blocking for…

Answer 25

Experimental designs

Question 26

Use stratifying and clustering for…

Answer 26

Observational studies

Question 27

Mutually exclusive

Answer 27

Probability for A or B (A U B); cannot occur together
- think ADDITION
- If there’s an overlap, subtract

Question 28

Independent

Answer 28

Probability A and B; one thing does not affect the other
- think MULTIPLY
- If A already happened; what’s the probability of second

Question 29

How to find probability when given percentages

Answer 29

Tree diagram

Question 30

Interpret probability (A) (mutually exclusive)

Answer 30

After many, many (context), the proportion of times that (context A) will occur is about (P(A)).

Question 31

Describing binomial distribution

Answer 31

Conditions: BINS
1) Binary - success or failure
2) Independent
3) Number of trials fixed - n = ___
4) Same probability - p = ___

• Shape - (np ≥ 10, n(1-p) ≥ 10)
• Center - mean: μx = np
• Variance - SD: ox = √np(1-p)

Question 32

Calculate binomial probability (exactly)

Answer 32

binompdf
(clearly identify parameters)

Question 33

Calculate binomial (a least)

Answer 33

1 - binompdf
(clearly identify parameters)

Question 34

Interpret conditional probability (independence)

Answer 34

Given (context B), there is a P(A|B) probability of (context A)

Question 35

Interpret expected value (mean, μ)

Answer 35

If the random process of (context) is repeated many times, the average number of (x context) we can expect is (expected value).

Question 36

Interpret binomial mean (μx)

Answer 36

After many, many trials, the average number of (success context) out of (n) is (μx).

Question 37

Interpret binomial SD (ox)

Answer 37

The number of (success context) out of (n) typically varies by (ox) from the mean of (μx).

Question 38

Transforming random variables (multiple/divide by A)

Answer 38

• Mean - multiply or divide by A
• SD - multiply or divide by A
• Variance - multiply or divide the SD by A^2

Question 39

Transforming random variables (add/subtract A)

Answer 39

• Mean - add or subtract by A
• SD - no change
• Variance - no change

Question 40

Combining random variables (S = X + Y)

Answer 40

• μ = μx + μy
• o = √ox^2 + oy^2
• o = ox^2 + oy^2

Question 41

Combining random variables (D = X - Y)

Answer 41

• μ = μx - μy
• o = √ox^2 + oy^2
• o = ox^2 + oy^2

Question 42

Calculate normal distribution probability (more/less than)

Answer 42

normalcdf(>, <, μ, o)

Question 43

Calculate normal distribution (gives % on curve)

Answer 43

inversecdf(area, μ, o)

Question 44

Identifying when to use geometric distributions

Answer 44

“On any given ___, there is a ___% probability…”

Question 45

Describing a geometric distribution

Answer 45

Conditions: BIFS
- Binary - success or failures
- Independence
- First success
- Same probability

• Shape
• Center - μx = 1/p
• Variability - ox = √(1-p)/p

Question 46

Find the probability of a geometric distribution (until)

Answer 46

geometricpdf(p, x)

Question 47

Find the probability of a geometric distribution (within)

Answer 47

geometriccdf(p, lower, upper)

Question 48

Sampling distribution

Answer 48

Many, many samples and a statistic calculated for each of those samples

Question 49

What makes a good statistic?

Answer 49

• No bias
• Low variability

Question 50

Z score for one sample proportion

Answer 50

z = (p (hat) - p) / √p(1-p)/n

Question 51

Z score for one sample mean

Answer 51

z = (x̄ - μ) / o/√n

Question 52

Calculate z score into p-value

Answer 52

normcdf(z score, 1E99, 0, 1)

Question 53

Interpret standard deviation of sample proportions (op(hat))

Answer 53

The sample proportion of (success context) typically varies by (op(hat)) from the true proportion of (p).

Question 54

Standard deviation of sample means (ox̄)

Answer 54

The sample mean amount of (x-context) typically varies by (ox̄) from the true mean of (μx).

Question 55

One sample confidence interval for mean (μ)

Answer 55

1) State: μ = true mean (context)
CL = ___
2) Plan: name: one sample t interval for μ
Conditions: 1) random
2) 10% rule
3) normal - pop. distribution is normal,
CLT (n ≥ 30), graph shows no strong
skew or outliers
3) Do: x +/- t* (S/√n)
4) Conclude: We are (CL)% confident that the interval
from ___ to ___ captures the true mean of (context).

Question 56

One sample confidence interval for proportions (p)

Answer 56

1) State: p = true proportion (context)
CL = ___
2) Plan: name: one sample z interval for p
Conditions: 1) random
2) 10% rule
3) normal - CLT (n ≥ 30)
3) Do: p(hat) +/- z* (√(p(hat)(1-p(hat))/n
4) Conclude: We are (CL)% confident that the interval
from ___ to ___ captures the true proportion of
(context).