APStats Interpretations

Shoutout to JB Hanson!

y-intercept

If 0 of x, we predict y will be …

Slope

For each 1 increase in x, we predict a … increase in y

SEb

Our sample slope will typically be … away from the true slope of y vs x.

t-score

Our sample slope was … standard deviations above the hypothesized slope of 0

S (standard deviations above the of residuals)

The actual y will typically deviate from the predicted x by …

P-value

A value of … indicates that if the null hypothesis is true, we would obtain a sample slope as extreme as ours less than .001 of the time due to random chance alone.

r²

95% of the variability in y can be explained by x.

Interpretation of the correlation r=.9

There is a strong positive linear relationship between y and x

Interval(.5,1.5)

We’re 95% confident the interval .5 to 1.5 captures the true proportion of (context)

95% confidence level

If we repeated this process many time, 95% of all calculated intervals would correctly capture the true proportion of (context)

Z-value

Our sample proportion was … std devs below/above the hypothesized proportion of …%

P-value

If the null hypothesis is true, then we would obtain a sample as extreme as ours …% of the time due to random chance alone

Phat

…% of context(students) in the sample are context(drug and alcohol free)

n

Our sample consists of … students

Hypothesis test

We have statistically significant evidence that the proportion of context(LZHS students who are drug and alcohol free) is less than .75

What does “statistically significant” mean?

Obtaining a sample as extreme as ours is unlikely to occur due to random chance alone

Central limit theorem

As the sample size increases, the sampling distribution’s shape becomes more normal, the mean stays the same, and the standard deviation directly decreases

Law of Large Numbers

As the sample size increases, the sample mean approaches the population mean.

Binomial Coefficient (4/2) =6

There are 6 ways to arrange 2 bullseyes out of the next 4 throws

Expected # of successes

The darts player is expected to hit .8 bullseyes, on average, for every 4 throws.

Interpret the distribution

The distribution of differences in vertical jumps is skewed left with a mean of about 0 and a range of 5.