STT315 Chapter 6 Inferences Based on a Single Sample
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Topics:
1. Identifying and Estimating the Target Parameter
2. Confidence Interval for a Population Mean: Normal (z) Statistic
3. Confidence Interval for a Population Mean: Student’s t-Statistic
4. Large-Sample Confidence Interval for a Population Proportion
5. Determining the Sample Size
Learning Objectives:
1. Estimate a population parameter (means, proportion, or variance) based on a
large sample selected from the population
2. Use the sampling distribution of a statistic to form a confidence interval for the
population parameter
3. Show how to select the proper sample size for estimating a population
parameter
6.1 Identifying and Estimating the Target Parameter
Target parameters - NOTATION:
- population mean
2
- population variance
p - population proportion
Introductory concepts (review)
Parameter – a numerical feature of a population
Target Parameter: population mean, population proportion, population variance
– any parameter we are interested in estimating
Statistic is any numerical measure calculated from data: the proportion, mean,
median, range, variance, standard deviation, etc.
Statistical inference: a method that converts the information from random
samples into reliable estimates of the population parameters.
A point estimate: a single number calculated from a sample that can be
regarded as an educated guess for an unknown population parameter.
A point estimator of a population parameter is a rule or formula that tells us
how to use the sample data to calculate a single number that can be used as an
estimate of the target parameter
Goal: Use the sampling distribution of a statistic to estimate the value of a
population parameter with a known degree of certainty.