SP 225 Lecture 11 Confidence Intervals

Three Separate Distributions Sample distribution Empirical and known Intended to help learn about the population Population distribution Empirical and unknown Properties estimated using statistics Sampling distribution Theoretical or non-empirical Properties well-known and based on probabilities

Example Problem A researcher has gathered information from a population with an average of 2.3 people and a standard deviation of 0.35. If the researcher collects samples of 100 households, what proportion of samples will have a mean less that 2.25?

Confidence Interval Mathematical statement that says that the parameter lies within a certain range of values 95% confident that the mean length of employment at XYZ automotive is between 8 and 12 years

Probability Distribution for Population Mean 95% confident that the mean length of employment at XYZ automotive is between 8 and 12 years (sample)

Confidence Interval Example A random sample of 100 television programs contained an average of 2.37 acts of physical violence per program. The standard deviation of the number of acts of violence on television in the population is 3. At the 99% level, what is your estimate of the mean number of acts of violence for all television programs?

Confidence Interval Formula

Confidence Interval Estimate

Confidence Interval Example 2 A researcher has gathered information from a random sample of 178 households. The households averaged 6.0 hours of television viewing per day with a standard deviation in the sample of 3.0 hours. Construct a 90% confidence interval for the hours of television watched per day in the population.

Alpha Percent of confidence intervals that DO NOT contain the population mean over the long run Probability this confidence interval DOES NOT contain the population mean Width of confidence interval Complement of confidence level

Efficiency Extent to which the confidence interval clusters around the mean Width of the confidence interval Determined by population standard deviation and sample size

Confidence Intervals in SPSS Give a 95% confidence interval for the number of children in an American family using GSS data.

In-Class 7.7 a & b