Chapter 13: Statistics 2 Sample T-Test for Difference in Population Means

General Rules of Sampling Distribution x1-x2

General Properties of the Sampling Distribution (x1- 2)
Rule 1: U (x1 x2) = u1- u2
The differences in sample means tend to cluster around the actual difference in population means.
Rule 2: The value of the standard error describes how much the x1 and x2 v

If sample sizes are small:

USE NORMAL PROBABILITY PLOTS, DOTPLOTS, OR BOXPLOTS. (type in data, and calculate if sample sizes are less than 30)

P-Value:

How likely to observe sample data as extreme or more extreme than what was observed if the null hypothesis were true.

2 Sample T-Test for Difference in Population Means 4 Key Questions:

1. hypothesis Testing
2. sample data
3. 1 numerical variable
4. and two independently selected samples.

2 Sample T-Test for Difference in Population means

Define the Hypothesis Testing: what is the mean for the samples, and the null and alternative hypothesis
Appropriate to use if you assume that population distributions are approximately normal.
Method: 4 Key Questions: hypothesis testing, sample data, one

Type 1 Error

Type 1 Error: Choosing (wrong) alternative hypothesis (rejecting true null hypothesis) (HA)

Type 2 Error

Type 2 Error: Choosing the (wrong) null hypothesis (failing to reject false null hypothesis) (HO)

Independent Samples

Selection of the individuals who make up one sample does not influence the selection of the individuals in the other sample.

How to tell if sample data is normally distributed:

Generally, the sampling distribution will be approximately normal if any of the following conditions apply.
-The population distribution is normal.
-The sample data are symmetric, unimodal, without outliers.
-The sample size is greater than 30, without ou

When to change the significance level?

When stated in the question or;

Conservative Estimate of P-Value

Alternative approach is a P-value that is close to but larger than the actual P-Value. If the null hypothesis is rejected using this estimate, then it will also reject the actual P-value used.
Formula:
t curve with degrees of freedom = to the smaller of (

The Pooled T-Test

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