a) What is the difference between a normal distribution and a standard normal distribution?
A normal distribution is the way that scores tend to distribute themselves around a mean. Many variables tend to form a rough bell curve surrounding their mean and tapering to the ends based on the standard deviation. A standardized normal distribution is the distribution you get when you transform the values of a variable in question to a standardized score such as a z score.
b) What is the purpose of using a standard normal distribution instead of the normal distribution?
If you want to look up a given value in a normal distribution to see what area of the curve it falls under, you would have to create a new normal distribution table for every possible mean and standard deviation. By converting to standard scores and using the standardized normal distribution, you can use a single table that has already been calculated.
c) Please cite one example of how the standard normal distribution is used, including the Z-values for your example.
If you have a z score of 2.00, the table shows that the distance between the mean (z=1.00) and the z of 2.00 is 0.4772. Since half of the scores are below the mean of 1, it means the total area of the curve below z = 2 is 0.9772. The remainder, the area above 2.00 is .0228, which is significant at p = .05
d) If you are given the level of significance, how do you obtain the critical value? You look it up in the Z table. If you are given a significance level of p = .05, you decide if you need a one or two tailed significance level (one tail if you are predicting a direction). If two tailed, you look in the table and double the significance level then look for the critical value of z. For example, two-tailed critical value for p = .05 is 1.96 because it is .025 times 2.
e) How are z-values related to hypothesis testing? They allow you to determine if the values derived are beyond t...