Question

The z distribution applied to admiration ratings: A sample of 148 of our statistics students rated their level of admiration for Hillary Clinton on a scale of 1 to 7. The mean rating was 4.06, and the standard deviation was 1.70. (For this exercise, treat this sample as the entire population of interest.) Use these data to demonstrate that the mean of the z distribution is always 0. Use these data to demonstrate that the standard deviation of the z distribution is always 1. Calculate the z score for a student who rated his admiration of Hillary Clinton as 6.1. A student had a z score of −0.55. What rating did she give for her admiration of Hillary Clinton?

Answer 1

Solution:
Given in the question
No. of sample = 148, we will treat this as population
Mean = 4.06
Standard deviation = 1.70
For Standardized test or Z distribution
Mean = 0
Standard deviation = 1
Solution(a)
We need to calculate Z-score for a student who rated his admiration of Hillary Clinton as 6.1
Z = (X-mean)/SD = (6.1-4.06)/1.70 = 2.04/1.70 = 1.2
So Z-score = 1.2 for a student who rated his admiration of Hillary Clinton as 6.1
Solution(b)
Z = -0.55
Rating at Z=-0.55
Z = (X-mean)/SD
-0.55 = (X-4.06)/1.70
-0.935 = X - 4.06
X = 3.125
So A student had a Z score of -0.55, she give 3.125 rating for her admiration of Hillary Clinton.