Chapter 11- Confidence Intervals for Univariate Data. Math 22 Introductory Statistics. Introduction into Estimation. Point Estimate – the value of a sample statistic used to estimate the population parameter.
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estimate margin of error
Three determinations must be made to develop a Confidence Interval:
Q: What does a 99% C.I. really mean?
A: A 99% C.I. means that of 100 different intervals obtained from 100 different samples, it is likely 99 of those intervals will contain the true parameter and one will not.
Two ways to reduce the margin of error:
(Problem - Reduces Validity)
For small sample sizes:
If the sample size is less than 30, construct a normal plot of your data. If your data appears to be from a normal distribution, then use the t-distribution. If the data does not appear to be normal, then use a non-parametric technique that will be introduced later.
For large sample sizes:
If the sample size is 30 or more, use the t-distribution citing the Central Limit theorem as justification for having satisfied the required assumption of normality.
Large Sample Confidence Interval for the Median:
Basic steps for conducting a large sample confidence interval for the median:
Basic steps for conducting a small sample confidence interval for the median: