**Chapter
5: Hypothesis Tests with Means of
Samples**

**The Distribution of Means**

## n
**Comparison distributions considered so far were
distributions of individual scores**

## n
**Mean of a group of scores**

### n
**Comparison distribution is distribution of means**

**The Distribution of Means**

## n
**Distribution of means**

### n
**Distribution of the means of each of a very large
number of samples of the same size (with each sample randomly taken from the
same population of individuals)**

**The Distribution of Means**

## n
**Characteristics**

### n
**Its mean is the same as the mean of the population of
individuals**

### n
**Its variance is the variance of the population divided
by the number of individuals in each of the samples**

**The Distribution of Means**

## n
**Characteristics**

### n
**Its standard deviation is the square root of its
variance**

### n
**Shape: it is approximately normal if either:**

#### n
**Each sample is of 30 or more individuals or**

#### n
**The distribution of the population of individuals is
normal**

**Review of the Different Kinds of Distributions**

## n
**Distribution of a population of individuals**

## n
**Distribution of a particular sample**

## n
**Distribution of means**

**Comparison of Three Types of Distributions**

** **

**Hypothesis Testing With a Distribution of Means**

## n
**It is the comparison distribution when a sample has
more than one individual**

## n
**Find a ***Z* score of your sample’s mean on a
distribution of means

** **

**Estimation, Standard Errors, and Confidence Intervals**

## n
**Estimating the mean: point estimates**

## n
**Accuracy of a point estimate**

## n
**Interval estimates**

### n
**Confidence limits**

### n
**95% confidence interval**

### n
**99% confidence interval**

**Estimation, Standard Errors, and Confidence Intervals**

## n
**Steps for figuring confidence limits**

** 1. Figure the standard error**

** **

** **

** **

** 2. Figure the raw scores for 1.96
standard errors (95% confidence interval)
or 2.57 standard errors (99% confidence
interval) above and below the
sample mean**

** **

**Estimation, Standard Errors, and Confidence Intervals**

## n
**Subtle logic of hypothesis testing**

## n
**Confidence intervals and hypothesis testing**

**Controversies and
Limitations**

## n
**Confidence intervals or significance tests?**

### n
**Confidence intervals **

#### n
**Give additional information**

#### n
**Focus attention on estimation**

#### n
**Less likely to be misused by researchers**

### n
**Significance tests**

#### n
**Necessary for some advanced statistical procedures**

**Reporting in
Research Articles**

## n
*Z*** test**

## n
**Standard error, ***SE*, *SEM*

### n
**Standard error bars**