Sampling Distributions, z-test

Question 1

What is the definition of sampling distribution of a statistic?

Answer 1

The 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 it resulted from chance alone.

Question 2

What are the two steps involved in data analysis?

Answer 2

1. Calculating the appropriate statistic – for example, number of pluses and minuses for the sign test
2. Evaluating the statistic based on its sampling distribution

Question 3

How do we derive the sampling distributions of the statistic? (3 steps)

Answer 3

1. Determining all the possible different samples of size N that can be formed from the population of scores
2. Calculating the statistic for each of the samples
3. Calculating the probability of getting each value of the statistic if chance alone is operating

Note that N = the size of each sample, not the number of samples

Question 4

What is the null-hypothesis population?

Answer 4

The null-hypothesis population is an actual or theoretical set of population scores that would result if the experiment were done on the entire population and the independent variable had no effect. It is called the null-hypothesis population because it is used to test the validity of the null hypothesis.

Question 5

What is the sampling distribution of the mean?

Answer 5

The sampling distribution of the mean gives all the values the mean can take, along with the probability of getting each value if sampling is random from the null-hypothesis population.

Question 5

Define the sampling distribution.

Answer 5

A sampling distribution gives all the values a statistic can take, along with the probability of getting each value if sampling is random from the null-hypothesis population.

Question 5

What does the central limit theorem tell us?

Answer 5

Regardless of the shape of the population of raw scores, the sampling distribution of the mean approaches as normal distribution as sample size N increases.
The further the raw scores deviate from normality, the larger the sample size must be for the sampling distribution of the mean to be normally shaped.
N大于等于30, it is usually assumed that the sampling distribution of the mean is normally shaped.

Question 5

What is the critical region for rejection of the null hypothesis?

Answer 5

It is the area under the curve that contains all the values of the statistic that allow rejection of the null hypothesis.

Determined by the alpha level. a = 0.05(1 tail) = z-score of +- 1.645
a = 0.05 (2-tailed) = z-score of +- 1.96

Question 6

What is the critical value of a statistic?

Answer 6

The value of the statistic that bounds the critical region.

Question 7

If the absolute value of zobt is greater or equal to the absolute value of zcrit, what do we do?

Answer 7

Reject H0.