Ch 12: Sampling Distributions & Normal Deviate test

1. Introduction

2. Sampling Distribution of a statistic defined:

a sampling distribution of a statistic gives 1) all the values that the statistic can take and

2) the probability of getting each value under the assumption that the value occurred by chance.

A. Sign test

B. Generating a sampling distribution of the mean

- i. Start with a population of raw scores, with m & s.

- ii. Draw all possible samples of a given sample size

- iii. Calculate the mean of each sample

- iv. Calculate the probability of getting each mean value if each mean occurred by chance.

Example: Given the population scores of 3,4,5,6,7 determine the sampling distribution of the
mean for N=2. Assume sampling with replacement.

C. Characteristics of the sampling distribution of the mean.

- i. There is a mean, standard deviation of the sampling distribution of the mean

- ii. The mean of the means (mean of sample means) is equal to the population mean

- iii. The standard deviation of the sampling distribution is related to the standard deviation of the population and the sample size :

- iv. Is normal, regardless of the shape of the population distribution, as long as N 30

3. The normal deviate test

A. probability of sampling a value from the normal distribution

B. The normal deviate test

- i. That value is the mean of the sample
- ii. The general( non-specific) null; The general (non-specific) alternative

- iii. The specific null; The specific alternative for the normal deviate test
- iv. Calculate the statistic

__v. Evaluate the statistic using the sampling distribution of the mean__

C. Evaluating the statistic using "critical region"

1. critical region: there is a region under the curve that contains all the values of the statistic that
allow for rejection of the null.

i. If z_{obt} falls within the critical region

ii. What is this region? It is determined by alpha

iii. Where does this region begin? It is determined by the critical value of the statistic, ie., the
value that bounds this region.

2. An economist wants to know if mean income has changed in ND over the last decade. In
1980 the values were mew=$10,000 and sd = 1500. She took a sample of 250 citizens and found
a mean income of 9623. What should she conclude?

Step 1: What are the hypotheses

step 2: find zobt

step 3: find zcrit

step 4: is |zobt| >= zcrit? If so reject null

4. Power and the normal deviate test.

A. Power

B. Steps

- 1. Find

2. __
__