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Mathematical Methods in the Physical Sciences
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardRepeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardQ.no.4 The test scores on the same algebra test were recorded for nine students randomly selected from a classroom taught by teacher A and eight students randomly selected from a classroom taught by Teacher B. Teacher A: 65, 88, 93, 95, 80, 76, 79, 77.Teacher B: 91, 85, 70, 82, 92, 68, 86, 87, 75. Test the hypothesis that the difference in the average scores for students taught by these two teachers equal to zero. Use 5% level of significance.arrow_forward
- Qn5. Using the Kruskal-Wallis test at a= 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I m =5, Sum of the ranks i.e., R, = 58 For System II:n, = 6, Sum of the ranks i.e., R, 24 For System III: n, = 8, Sum of the ranks i.e., R 87. ( Given that Table value of Chi Square = 9.21) %3Darrow_forwardA sample, with M=42 and n=64, is selected from a population with a μ=48 and σ=16. Would this sample be considered extreme and unrepresentative for this population?arrow_forwardQn5. Using the Kruskal-Wallis test at a = 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I: n = 5, Sum of the ranks i.e., R = 58 For System II:n, = 6, Sum of the ranks i.e., R, = 24 For System III: n, = 8, Sum of the ranks i.e., R, = 87. %3! ( Given that Table value of Chi Square = 9.21)arrow_forward
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- The proportion of adults living in a small town who are college graduates is estimated to be p = 0.5. To test this hypothesis, a random sample of 10 adults is selected. If the number of college graduates in the sample is anywhere from 3 to 7, we shall not reject the null hypothesis that p = 0.5; otherwise, we shall conclude that p + 0.5. Complete parts (a) through (c) below. Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. Click here to view page 3 of the table of binomial probability sums. %3D (a) Evaluate a assuming that p = 0.5. Use the binomial distribution. (Round to four decimal places as needed.)arrow_forwardRandom collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 12.35 9.83 10.79 11.31 8.58 13.69 14.68 15.07 11.57 Lab B (y) 12.18 9.72 10.70 11.51 8.63 13.58 14.71 15.24 11.57 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. Compound Lab A (x) Lab B (y) d = x − y d2 1 2 3 4 5 6 7 8 9 Σd2 = (b) Use a 5% level of significance to test for a monotone relation (either way) between ranks. Interpret the results. What is the level of significance? Compute the sample test statistic. (Round your answer to three decimal places.)arrow_forwardRandom collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 15.36 12.83 8.81 11.30 13.59 9.66 10.72 14.05 11.54 Lab B (y) 15.17 12.72 8.69 11.45 13.63 9.63 10.75 14.23 11.55 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. (b) Compute the sample test statistic. (Round your answer to three decimal places.)arrow_forward
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