Chapter 6 Confidence Interval Estimates

the process of determining a likely value for a population parameter.

for a population parameter is a single-valued estimate of that parameter; the population mean or proportion.

estimate; a range of values that are likely to cover the true population parameter with a level of confidence attached, such as 95% confidence that the interval contains the unknown parameter.

the general form of confidence interval.

Point estimate and confidence interval.

Dichotomous or continuous.

dictate the appropriate estimation technique.

90%, 95%, and 99%. Although any level can be chosen between 0 & 100%.

Point estimate

There is a 95% probability that a confidence interval will contain the true population mean.

(for 95% confidence level) X +/- (z)1.96 σ/√n

(for 95% confidence level) 1.96 σ/√n

z values - which translate to larger margins of error and wider confidence intervals.

a wider interval.

smaller samples, resulting in larger margins of error. There is more imprecision with small samples.

95 out of 100 confidence intervals will contain the true mean value μ, and 5 out of 100 will not include the true mean value.

s

We are 90%, 95%, 99% confident that the true mean in the population is between a and b.

p̂ +/- z√p̂1 (1-p̂)/n

SE(p̂) = √p̂1 (1-p̂)/n

We are 90%, 95%, 99% confident that the true proportion is between a and b.

The sample mean

1. how confident you want to be in the estimate, 2. standard deviation in the underlying population, 3. the size of the sample

the wider your confidence interval will be.

the farther the confidence interval will deviate from the mean which means a wider interval.

the higher the accuracy.

1. level of confidence (z or t, the bigger the confidence level the higher the margin of error), 2. standard deviation (bigger the sigma, the higher the margin of error), 3. sample size (the smaller the sample, the larger the margin of error).