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normal distribution
a frequency distribution that is shaped like a symmetrical bell, unimodal curve
total relative frequency of distribution
area under curve = 100% of the data or 1.0
68% of values
% fall within 1 standard deviation of mean
95% of values
% fall within 2 standard deviations of mean
99.7 % of values
fall with in 3 standard deviations of he mean
normal curve defined by
mean and standard deviation
raw score
exact value that is observed
standard score
indicates exactly how many standard deviations a raw score is above or below the
mean. Z-score
What is the purpose of calculating z-scores?
, The purpose of calculating z-scores is to understand a score's relative standing within a
distribution. The z-score standardizes scores from different data sets with different
means
formula for raw score to z-score
formula for z-score to raw score
formula for sample mean to z-score
divided by standard error o/square root of sample
standard normal table
Shows the proportion of values that fall to the left (or below) of a given z-score in a
normal distribution
How to find percentage above z-score
1- p-value
hypothesis testing using a z-score
1) State the null (H0 ) and alternative (Ha ) hypotheses.
2) Determine the critical values.
3) Calculate the z-score.
4) Compare the z-score to the critical value and determine whether to reject H0.
one-tailed test
a directional test because it specifies whether the population mean increases or
decreases after the treatment (can be left or right tail)
left tail
decreases, Ha:u<55
right tail