Confidence Intervals for a Population Mean Standard Deviation

Confidence Intervals for a Population Mean, Standard Deviation Known

Assumptions 1. Sigma, aka population standard deviation is known 2. n > 30 (large sample) or population follows a normal distribution 3. Sample is a simple random sample (equal chance of being selected)

Definitions Point estimate = a single value (or point) used to approximate a population parameter. Note: sample mean is the best point estimate of the population mean Confidence interval = a range or an interval of values used to estimate the true value of a population parameter

Definitions Margin of error = diff. between observed sample mean and the true value of the population mean “E” aka “maximum error of the estimate”

Interpreting a confidence interval We are 95% confident that the interval from 98. 08 to 98. 32 actually does contain the true value of the population mean.

TI-83/84 Instructions TI-83 Finding confidence intervals 1. “Stat” button 2. Choose “Tests” Menu 3. Choose “ZInterval” 4. Highlight “Stats” 5. Enter std dev, mean, n, and C-level 6. “Highlight Calculate” and press “Enter” Finding Margin of Error : Subtract smallest part of interval from mean.

Sample Size to Estimate Population Mean = critical z score based on desired degree of confidence E = desired margin of error = population standard deviation

Example 01 Finding critical z score: Lets find the critical z score for 96% confidence

Example 01 Finding critical z score: Lets find the critical z score for 96% confidence

Example 01 Finding critical z score: We are trying to find the z, so looking at it from left to right, we are interested in 98% or

Example 01 Finding critical z score: So we find it by using: INVNORM(. 98, 0, 1) = 2. 053748911

Range Rule of Thumb: If Sigma Isn’t Given Note: When finding the sample size, always round up if any decimals

Confidence Interval (By Hand)