More Statistics

Z-Score and the Bell Shaped Curve

Z-Table

Example: Find the area of the shaded region.

The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

A graph with a bell-shaped curve, divided into 2 regions by a line from top to bottom on the right side. The region left of the line is shaded. The z-axis below the line is labeled "z=0.98".

OK – I have a drawing for you – it shows the bell shaped curve – and the z formula of z = .98 which is less than 1 standard deviation When we look at the Z chart and look up .98 it gives us .8365

.8365 is the area shaded under the bell shaped curve for a z score of .98

JilMac draws Bell Shaped Curve for Z=.98

CLT - Central Limit Theorem

http://www.investopedia.com/terms/c/central_limit_theorem.asp

Khan's definition https://www.khanacademy.org/math/statistics-probability/sampling-distributions-library/sample-means/v/central-limit-theorem

Sampling distribution and standard error http://stattrek.com/sampling/sampling-distribution.aspx

One-Way ANOVA table

    • df (between samples) = k-1 where k = number of samples

    • df (within samples) = T-k where T = number of treatments/type

Hypothesis Testing Example:

  • The American Mathematical Association claims that more than 40% of all people like statistics

  • The NULL hypothesis would read ... Ho: P = 0.4

  • The Alternative would read ... Ha : P > 0.4

Sample Size Calculator:

    • http://www.raosoft.com/samplesize.html