Chapter 7 -Normal Distributions & Probability

Question 1

Features of a Normal Distribution

Answer 1

1) Asymptotic tails (left and right tails continue to infinty)
2) Unimodal and symmetric (bell shaped)
3) Mean=0 and standard deviation=1

Question 2

Standard Normal Distribution (z-scores) vs Normal Distribution (any scores)

Answer 2

The standard normal distribution is a normal distribution of z-scores whereas the normal distribution can be a distribution of any scores from any measurement

Question 3

Why is probability important in research?

Answer 3

Researchers use probability to determine if a sample is likely or unlikely to occur in the population

Question 4

Distribution of sample means (DoSM

Answer 4

Collection of all sample means for all possible samples of a particular size selected from a specific population

Question 5

Standard Error of M

Answer 5

Measures the average distance (deviation) of the sample mean (M) from the population mean (µ)

Question 6

Main characteristics of the sampling distribution of the mean?

Answer 6

1) It will be normally distributed if the population was normally distributed or if n > 30
2) The mean of the distribution of sample means will equal the population mean, μ;
3) The standard deviation of the distribution of sample means is equal to the standard error of the mean, σM = σ/√n

Question 7

What does the standard error of M measures?

Answer 7

How well an individual sample mean represents the entire distribution

Question 8

Variability of a distribution of scores is measured by ________-

Answer 8

standard deviation

Question 9

Law of large numbers

Answer 9

The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean

Question 10

The smaller the variance in the population, the more probable it is that __________

Answer 10

The sample mean will be close to the population mean

Question 11

Standard error of the sampling distribution of the means decreases as _________

Answer 11

Sample size increases

Question 12

Standard deviation vs standard error

Answer 12

Standard deviation measures the distance between individual scores and the mean, while standard error measures the distance between sample means and the population mean.

Question 13

If the test statistic is more extreme than the critical value, the null hypothesis _____

If test statistic is less than the critical value, then we ________

Answer 13

is rejected; fail to reject the null hypothesis