AP Statistics Interpret Statements

Interpret mean

If many, many are randomly selected, their will be, on average, about

Interpret standard deviation

The typically varies by about from the mean of

Interpret percentile

of were less than or equal to

Interpret z score

The is standard deviation the average in the sample.

Interpret probability

If you take a very large random sample of about

% of them will be

Interpret confidence level

If we select many random samples of the same size from the same population and construct a % confidence interval using each sample, about % of the intervals would capture the true .

Interpret confidence Interval

We are % confident that the interval from to captures the true

Interpret slope

For every of one of , there is an average of of .

Interpret y-intercept

When the is 0 it is predicted that the would be .

Interpret r (correlation coefficient)

The correlation coefficient of indicates there is a , linear relationship between and .

Interpret r2 (coefficient of determination)

% of variability in can be explained by the linear relationship with .

Interpret standard deviation of the residual

The is typically about away from the predicted by the LSRL with x =

Interpret the standard deviation of the sampling distribution

In SRSs of size , the sample of will typically vary by about <σp̂/σx̄> from the true of <µ/p> .

Interpret P-value

Assuming that the , there is a probability of getting a sample of or just by chance in a random sample of

Interpret P-value for difference

If there is no difference in the true of , there is a % probability of getting a difference in the as large as or larger than the one observed () by chance alone

Interpret the power of the test

If the true is , there is a probability that the will find convincing evidence for Ha: .

Interpret the power of the test (alternative)

If power=, then the probability of correctly rejecting the is %.

Interpret the standard error of the estimated slope (SEb or sb)

The slope typically varies by about when predicting the from the

Conclusion of a significance test: P

Since the P-value = [value] < alpha = [significance level], we reject the Ho. There IS convincing evidence [for the Ha in context].

Conclusion of a significance test: P>a

Since the P-value = [value] > alpha = [significance level], we fail to reject the Ho. There is NOT convincing evidence [for the Ha in context].

Standard error of slope

If we took many random samples of size [n] and calculated the slope of each sample, the sample slopes typically varies from the population (true) slope by [value].

Single residual for an x value

The LSRL underpredicted/overpredicted the value of [y in context] by [the residual amount.].

Conclusion of a confidence interval

We are % confident that the interval from to captures the true