ap stats unit 6 vocab c

Conditions for Constructing a Confidence Interval for a Difference between Two Proportions (Fill in the blank.)

Random, 10% (for both sample size ns so 2), and Large Counts

Random

The data come from two independent random samples or from two groups in a randomized experiment.

10%

When sampling without replacement, n1 < 0.10N1 and n2 < 0.10N2.

Large Counts (for Confid Interval)

The counts of “successes” and “failures” in each sample or group – n1p^1, n1(1 – p^1), n2p^2, and n2(1 – p^2) – are all at least 10.

Standard error for p1 – p2

sp^1 – p^2 = square root (((p^1(1-p^1))/n1) + ((p^2(1-p^2))/n2))

C% confidence interval for p1 – p2

(p^1 – p^2) +- z* (square root (((p^1(1-p^1))/n1) + ((p^2(1-p^2))/n2)))

Two–sample z interval for a difference in proportions

A confidence interval used to estimate a difference in the proportions of successes for two populations or treatments.

Pooled sample proportion

Another name for combined sample proportion.

Combined sample proportion

p^C = (x1 +x2)/(n1 + n2) = (n1p^1 + n2p^2)/(n1 + n2)

p^C

Variable for combined sample proportion.

Conditions for Performing a Significance Test about a Difference between Two Proportions (Fill in the blank.)

Random, 10% (for both ns), and Large Counts (p^C)

Large Counts (for Sig Test between two)

The expected numbers of successes and failures in each sample or group – n1p^C, n1(1 – p^C), n2p^C, and n2(1 – p^C) – are all at least 10.

Z statistic for two–sample z test

z = ((p^1 – p^2) – 0)/ square root (p^C (1-p^C)((1/n1) + (1/n2))

Two–sample z test for a difference in a proportions

z = ((p^1 – p^2) – 0)/ square root (p^C(1-p^C)((1/n1) + (1/n2)) where p^C = (x1 +x2)/(n1 + n2)