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. 27.3 34.6 30.6 27.8 33.4 31.5 27.3 31.2 32.0 24.7 24.4 28.2 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.
Added by Brian R.
Step 1
- List: 27.3, 34.6, 30.6, 27.8, 33.4, 31.5, 27.3, 31.2, 32.0, 24.7, 24.4, 28.2 - Sort: 24.4, 24.7, 27.3, 27.3, 27.8, 28.2, 30.6, 31.2, 31.5, 32.0, 33.4, 34.6 - For n = 12, median = (6th + 7th values)/2 = (28.2 + 30.6)/2 = 29.4 Show more…
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Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (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. (d) Conclude the test. (e) Interpret the conclusion in the context of the application. 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 $15 \mathrm{cm}$ deep, were studied and the following percentages of sand in the soil were recorded. $$\begin{array}{rrrrrrrrrr} 19.0 & 27.0 & 30.0 & 24.3 & 33.2 & 27.5 & 24.2 & 18.0 & 16.2 & 8.3 & 1.0 & 0.0 \end{array}$$ (i) Convert this sequence of numbers to a sequence of symbols $A$ and $B$, where A indicates a value above the median and B a value below the median. (ii) Test the sequence for randomness about the median. Use $\alpha=0.05$.
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Runs Test for Randomness
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (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. (d) Conclude the test. (e) Interpret the conclusion in the context of the application. 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 $15 \mathrm{cm}$ deep, were studied and the following percentages of clay in the soil were recorded. $$\begin{array}{rrrrrrrrr} 47.4 & 43.4 & 48.4 & 42.6 & 41.4 & 40.7 & 46.4 & 44.8 & 36.5 & 35.7 & 33.7 & 42.6 \end{array}$$ (i) Convert this sequence of numbers to a sequence of symbols $A$ and $B$, where A indicates a value above the median and B a value below the median. (ii) Test the sequence for randomness about the median. Use $\alpha=0.05$.
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (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. (d) Conclude the test. (e) Interpret the conclusion in the context of the application. Civil Engineering: Soil Profiles 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 $15 \mathrm{~cm}$ deep, were studied and the following percentages of sand in the soil were recorded. $\begin{array}{llllllllllll}19.0 & 27.0 & 30.0 & 24.3 & 33.2 & 27.5 & 24.2 & 18.0 & 16.2 & 8.3 & 1.0 & 0.0\end{array}$ (i) Convert this sequence of numbers to a sequence of symbols $A$ and $B$, where A indicates a value above the median and B a value below the median. (ii) Test the sequence for randomness about the median. Use $\alpha=0.05$.
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