Tony

Yen and the art of learning statistics without really trying Comparing 2 sample mean or [proportions.

Rose

Programs Inference on 2 sample statistics / parameters:

Rose and Tony are continuing their discussion on Statistical Inference in James White Library.

Tony: "I did what you suggested, I reviewed Confidence Intervals on comparing sample mean or proportion to the population parameters
and summarized the following:"

"The Confidence Interval is just the sample statistics, like the mean plus or minus the table statistics
(z-score or t-table value depending on the sample size) times the sample standard deviation."
 

Sample size, n	Confidence Interval
	Lower Limit	Upper Limit
Use t-test
Use z-score	or	or

Here is a summary of the test statistics and decision criteria for comparing sample mean and proportion to the corresponding population
parameter:

Given H₀     or   (remember that the null hypothesis, H₀ is that the sample statistics equals the population parameter).
 

If the Ha is	Sample size	Test Statistics	Accept Null Hypothesis if P-value > a  or test statistics
or	Large	or
	Small
or	Large
	Small
or	Large
	Small

Rose: "You did well, this is often a very difficult topic to comprehend, but once mastered it will allow you to understand more
complicated inference problems more readily."

"Often the population parameter is not know, but you may use past data or statistics from samples over a long period of time to
estimate its true value."

"A more common inference is when you need to compare two sample statistics such as the means and proportions of two set of data."

"The principle is the same, as comparing the sample statistics with a population parameter; however, the formulas for both the standard error and the test statistics are more complicated."

"Try knowing when to use appropriate formulas for 2-sample statistics comparisons by studying the following summary:"

2 - Sample Statistics Summary

"See if you can learn how to make inference or decisions from examples using the interactive programs below"

Examples of 2 Sample Statistical Inference.

Programs for finding Statistics to make Inference about 2 sample statistics.

"Follow these steps in making decisions about two sample statistics:"

Step 1. Determine from the sample size (smallest sample size) which test to use: either t-test or z-score.

Step 2. Compute or Enter Statistics for both samples in program: to calculate 2-sample standard error and test statistics.

Step 3. Make your decision to accept or reject the null hypothesis by using either the P-value or by comparing the calculated or observed
test statistics with the test statistics obtained from the statistics table (using appropriate alpha values and degree of freedom -
alpha for 2-tail or alpha / 2 for 1-tail test).

Tony: "Twice in one day you have given me assignments to do."

Rose: "The only way to learn how to make statistical decisions is to make lots of them!"