Essential Statistics Chapter 16 1

Review Part III_A_Chi

Z-procedure Vs t-procedure

Standard error (SE)

Confidence interval

Essential Statistics Chapter 18 2

n

ppSE

ˆˆ

1

n

ppzp

ˆˆˆ 1

Standard Error & Confidence Interval In Proportions

Test Statistic for Proportions

Z test statisticH0: p = p0

Single sided

Ha: p > p0

Ha: p < p0

Double sided

Ha: p ≠ p0

Essential Statistics Chapter 18 3

n)p(p

pp̂z

00

0

1

Essential Statistics Chapter 21 4

To determine if the differences between the observed counts and expected counts are statistically significant (to show a real relationship between the two categorical variables), we use the chi-square statistic:

Chi-Square Statistic

count expected

count expectedcount observed 22X

where the sum is over all cells in the table.

Essential Statistics Chapter 21 5

The expected count in any cell of a two-way table (when H0 is true) is

Chi-Square Statistic:Expected Counts

total tabletotal) (column total)(row count expected

Essential Statistics Chapter 21 6

Chi-square test for a two-way table withr rows and c columns uses critical values from a chi-square distribution with(r 1)(c 1) degrees of freedom

P-value is the area to the right of X2 under the density curve of the chi-square distribution– use chi-square table

Degree of Freedom in Chi-Square Tests