Normal Curve and Introduction to Z

Topic 7

what is the normal curve/bell-shaped curve?

symmetrical curve that assumes the mean, median, and mode are equal, provides an inference for when comparing a sample to a population, tails are asymptotic which makes the bell curve platykurtic

what is the z-score?

the number of SDs the raw score is from the mean, they are comparable across distributions, scores below the mean are considered negative and scores above the mean are considered positive

what is the z-score formula?

X-X(mean)/SD

what does the area under a curve indicate for z-scores?

probabilities

how do z-scores connect to hypothesis testing?

standardize data for comparison, help determine how extreme or typical a sample statistic is

how do z-scores connect to null hypotheses?

z-scores define boundaries for accepting or rejecting the null hypothesis

what is the z-score for a 95% confidence interval?

±1.96

what do p-values represent?

the probability of obtaining a z-score as extreme as observed if the null hypothesis was true

what is an average value distribution?

average determines the peak of the distribution, shift in average moves the distribution along the axis, higher average can push the scores and distribution more positive (right) while lower averages can push the distribution more negatively and to the left

what is a variability distribution?

scores differing from the average,

what does skewness indicate?

prescence of extreme values

what does kurtosis indicate?

helps identify how extreme values affect the distribution

which has higher kurtosis, leptokurtic or platykurtic?

leptokurtic

which has lower kurtosis, leptokurtic or platykurtic?

platykurtic