Sand and clay studies were conducted at the West Side Field Station of the University of California. (Reference: Professor D. R. Nielsen, University of California, Davis.) Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 19.5 27.3 30.4 24.2 33.8 27.4 24.8 18.2 16.4 8.4 1.7 0.1 Test the sequence for randomness about the median. Use α = 0.05. (a) What is the level of significance? (b) Find the sample test statistic R, the number of runs. (c) Find the upper and lower critical values in Table 10 of Appendix II. c1 c2
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.
Sand and clay studies were conducted at the West Side Field Station of the University of California. (Reference: Professor D. R. Nielsen, University of California, Davis.) Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.
| 19.5 | 27.3 | 30.4 | 24.2 | 33.8 | 27.4 | 24.8 | 18.2 | 16.4 | 8.4 | 1.7 | 0.1 |
Test the sequence for randomness about the
(c) Find the upper and lower critical values in Table 10 of Appendix II.
| c1 | |
| c2 |
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