Basics of Z-Score and Normal Model and Variables
these variables fit this scale of measurement:
Olympic medal (gold, silver, bronze)
Military ranking (Captain, Major, Colonel, etc)
income level (low income, middle income, high income)
Education level (HS degree, BA, MA, PhD)
What is ordinal?
The average people in a calculus class in a college is 34 kids with a standard deviation of 2. What is the z-score of there being a class with 39 kids
what is 2.5?
0, 0, 10, 8 ,6, 4
What is 5?
(take the mean of 4 and 6)
these variables fit this scale of measurement:
social security number
school id number
types of cats
What is nominal?
Find z so that 50% of the mean is above z.
What is 0?
if 50% of scores is above z, the z is the mean, which is 0.
Elizabeth wants to know the average age of women getting married in the 1920s is different from the average age of women in 2020. If she is told that she is testing at the .05 level, what is the cut off score?
1.96 and -1.96
(two tailed test at .05 level)
Pam wants to know if age affects voting behavior.
This is an example of ____ statistics.
What is inferential?
If you are given a sample in which the model is normal and 95% of the values are included, how many standard deviations away from the mean should we expect the most extreme values within the 95% be
2 standard deviations
The mean grade on the test was 82 with a standard deviation of 6. If the model is normal what is the assumed cutoff grade that the top 5% of students in the class received for a grade
what is 91.8?
first, find the z for 5 in the tail on the z table.
the z = 1.64, then solve for x using the z.
The Hulk wants to know if men can lift more than women. He has calculated that the Z in his sample is 3 . If the cut off in his test is 2.33, what can he conclude about the test?
Hulk can conclude that men lift more than women. (3 is greater than 2.33, in the rejection region. can reject the null hypothesis that men don't lift more than women)
Without using a calculator, given that the model is normal, what percentage of values should lie over 1 standard deviation above the mean
16% ( 100-68=32, 32/2=16%) you divide by 2 since we are only looking at values over 1 standard deviation, and not including below 1 standard deviation.
The average test score in a class was a 85 with a standard deviation of 7. Ryan received a 75. The teacher said that the bottom 10% of the class would have to retake the test. Assuming that the model is normal, does Ryan have to retake the test?
yes
This measure of variation tells us how much data values deviate from the average/mean.
What is the standard deviation?
What is the probability that a kid gets a test grade that is 3 standard deviations below the mean, given that the model is normal
0.15% (100-99.7= 0.3%, 0.3/2=0.15%) we divide by 2 since we are only looking at values below 3 standard deviations, and we are not including above 3 standard deviations
The class quiz scores had a mean of 65 and a standard deviation of 5. You got a score of 70. What is the z score?
What is 1?
(70-65)/5 = 1
Mike finds that his test grade of 82 had a z-score of -1.5 and that the standard deviation of the grades in his class was 6. What was the mean test grade in his class
91