Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 19.3 27.8 24.2 19.9 27.0 26.5 19.5 28.2 27.3 19.1 17.8 21.8 Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results. Since the number of runs does not lie between the upper and lower critical values, the data are not statistically significant. Based on this, we reject the null hypothesis that the percentages of sand in the soil are not random. Since the number of runs lies between the upper and lower critical values, the data are statistically significant. Based on this, we reject the null hypothesis that the percentages of sand in the soil are not random. Since the number of runs lies between the upper and lower critical values, the data are not statistically significant. Based on this, we do not reject the null hypothesis that the percentages of sand in the soil are not random. Since the number of runs does not lie between the upper and lower critical values, the data are not statistically significant. Based on this, we do not reject the null hypothesis that the percentages of sand in the soil are not random. Since the number of runs lies between the upper and lower critical values, the data are statistically significant. Based on this, we do not reject the null hypothesis that the percentages of sand in the soil are not random.
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 a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.
|
19.3 |
27.8 |
24.2 |
19.9 |
27.0 |
26.5 |
|
19.5 |
28.2 |
27.3 |
19.1 |
17.8 |
21.8 |
Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results.
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