Stat 201: chapters 5 and 6

point estimation

the process of using a single sample value, to approximate an unknown population parameter

interval estimation

provides a range of values that is likely to contain an unknown parameter

sampling distribution

a probability distribution consisting of all possible values of a sample statistic

X-N

(u,𝜎)

x bar - N

(u, 𝜎/√n)

p hat -N

(p, √p(1-p)/n)

central limit theorem

as the size n of a simple random sample increases, the shape of the sampling distribution of x̄ tends toward being normally distributed, n ≥ 30 for population mean and np and n(1-p) ≥ 10 for population proportion

standard error

𝜎/√n or √p(1-p)/n

margin of error

critical value*standard error

critical value (Z)

z-score corresponding to desired confidence level

90%

1.645

95%

1.96

99%

2.576

confidence interval

a plausible range of values for the population parameter

confidence interval formula

point estimate +/- margin of error

width of confidence interval

twice the margin of error

CI for population mean

x bar + - z* 𝜎/√n

CI for population proportion

p hat + - z*√p(1-p)/n

sample size formula for population mean

n= (z* 𝜎 / m) ^2

sample size formula for population proportion

n = (z/m)^2 p(1-p)

confidence interval for u with unknown 𝜎 formula

x bar +- t(n-1) (s/√n)

degrees of freedom

n-1