AP Stat Sentences & Vocab

Levels

Values of the factor/dependent variable

Range

The highest value minus the lowest value (NOT the spread!)

Spread

The smallest value in the data to the largest value

IQR sentence

“The range of the middle half of (insert variable) is…”

Percentile

The value with n% of observations less than the stated percentile

Z-score sentence

(Insert point) is (insert z-score) standard deviations above/below the mean

Empirical rule

• ±1 SD = 68% of data

• ±2 SD = 95% of data

• ±3 SD = 99.7% of data

Normal distribution calculation procedure

1. Define x

   1. x ~ N

   2. Define X

   3. Write a probability statement

2. Write formula for z-score, substitute, and calculate

3. Find appropriate area

   1. Show a sketch if needed

4. Write a conclusion in context

Properties of correlation coefficient

• Changing units has no effect on r

• Correlation makes no distinction between the explanatory and response variable

Strength of correlation coefficient

• 1 - 0.8 = very strong

• 0.8 - 0.6 = strong

• 0.6 - 0.4 = moderate

• 0.4 - 0.2 = weak

• 0.2 - 0 = very weak

Residual equation

• Observed - predicted (y - y hat)

• Always passes through (x bar, y bar)

• Minimizes the sum of the squares of the residuals

Coefficient of determination sentence

“r²” percent of the variation in (the dependent variable) is explained by the LSRL

Interpreting s (LSRLs)

• “When using the LSRL, the predicted values of (dependent variable) will typically be off from the actual value by about (s)

Disjoint/mutually exclusive

• These two events cannot occur at the same time— if one happens, the other cannot

• They are DEPENDENT

Testing for independence

Independent if P(A|B) = P(A) and P(AnB) = P(A)*P(B)

Random variable

Any variable whose value is a numerical outcome of a random phenomenon

Discrete random variables

• Have a countable number of outcomes

Continuous random variable

• A variable that takes on the values in an interval of numbers

Steps to solve a binomial probability question

1. State the distribution B(n, p)

   1. May have to perform BINS

2. Define X

3. State the probability question

4. Perform the calculation

5. Answer in a sentence

Rule of thumb

• As n creases, the binomial distribution starts looking like a normal distribution

• np >= 10 and n(1-p) >= 10 → can use normal approximation

Sample distribution

The distribution of values for many random samples of size (n) and a statistic calculated from that sample

Central limit theorem

• If samples of size n (n>30) are drawn from ANY population with mean mew and standard deviation sigma, then the sampling distribution of sample means is normal

  • Greater sample size = better approximation

Confidence interval sentence

“We are C% confident that the interval… captures the true population proportion/mean”

Confidence level sentence

“If we take many, many samples and calculate a confidence interval for each, in about C% of all samples, we get an interval that captures the true parameter