Interval estimation

A. Parameters of the sampling distribution of the sample mean

; (standard error of the sample mean)

( estimator of the standard error if σ is unknown )

B. Confidence interval formulas for the population mean:

1. (σ is known) 2. ( use the z distribution if σ is unknown and n is large).

3. ( use the t-distribution if σ is unknown and n is small )

C. Parameters of the sampling distribution of the sample proportion

(In this section p refers to population proportion and refers to sample proportion. It is slightly different from the book notation. )

1. ; (standard error of the sample proportion)

D. Confidence interval formulas for the population proportion:

1. ; (large sample case. Since p is generally unknown, to find ,

we replace p by ).

E. Sample size determination formulas to estimate unknown parameters

1. for the mean

2. for the proportion . If there is no estimate for p, let p = 0.5.

STANDARDIZATION FORMULAS

1. 2. 3.