With 12 degrees of freedom, the values of xa12 = x°0.025 and x x0.975 can be found from a chi- square table. Area in Upper Tail Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.05 3.571 4.404 21.026 23.337| 26.217 28.300 12 3.074 5.226 6.304 18.549 To find the value of x²a/2 = x0.025, move along the row for 12 degrees of freedom until reaching the column for an upper tail area of 0.025. Find x.025, rounding the result to three decimal places. x0.025 =| Use this same process to find x6.975, rounding the result to three decimal places. x'0.975 %3D
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
 alt="With 12 degrees of freedom, the values of x/2 = x0.025 and x- a/2 = x0,975 can be found from a chi-
square table.
Area in Upper Tail
Degrees
of
Freedom
0.995
0.99
0.975
0.95
0.90
0.10
0.05
0.025
0.01
0.05
12
3.074
3.571
4.404
5.226
6.304
18.549
21.026
23.337
26.217
28.300
,2
= x0.025, move along the row for 12 degrees of freedom until reaching the column
To find the value of xa/2
for an upper tail area of 0.025. Find x0.025, rounding the result to three decimal places.
x0.025
Use this same process to find x0.975, rounding the result to three decimal places.
x0.975
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