Chapter #10: ESTIMATION - Test statistics- actual applications using the formulas on flow chart to Two population mean: we use the statistic Xbar1- Xbar2
Statistical inference- acquires info and draw conclusion about population determine results and using results to see if it falls in the rejection Two cases:
samples regions to make conclusion - two unknown population variances are equal
Estimation- objective is to determine value of population parameter using - P-value-can only find p-value manually when your dealing with z - two unknown population variances are not equal
sample statistics distribution You must do an F-TEST before you can tell if the variances are equal or not in an
Sample mean (Xbar) and estimate population mean (mu) o P-value of a test is probability of observing a test statistiindependent sample situation.
TWO types of inferences at least as extreme as the one computed, given that null
- Estimation and hypothesis testing hypothesis is true.
TWO types of estimator o The smaller the p value the more statistical evidence exists
- Point estimator- value unknown parameter using SINGLE VALUE OR PT to support alternative hypotheis.
Three drawbacks o Ex. Given mu=170 extreme values or Xbar= 178
o Virtually certain that estimate will be wrong ,P(z>178-170/ 65/root 400)=1-0.9931=0.0069
o Need to know how close to estimator is to parameter - Conclusion – statement about whether there is enough evidence and
o Do not reflect larger sample size or parameter value information to make assumptions or not in accordance to the
- Interval estimator (confidence interval)- draws inferences about population by confidence level.
estimating value of unknown parameter using interval EXAMPLE:
Qualities of Estimators- unbiased, consistency, relative efficiency
- Unbiased estimator- expected value is equal to parameter
E(X)=MU (cant tell how close to parameter)
- Consistency estimator- difference between estimator and parameter
grows smaller as ample gets larger
- Relative efficient estimator- if there are 2 unbiased estimators of a
parameter, the 1 variance smaller is said to have relative efficient Chapter 12: Inference about one population
The width of confidence interval When σ is unknown we conduct a t-test and estimator on mu where z becomes t
- Larger confidence level produces wider confidence intervals and σ becomes s in the equations.
- Larger value of σ produce wider confidence intervals The degrees of freedom – (a function of sample size) determines how spread the
- Larger sample size, narrow confidence interval distribution is (compared to the normal distribu