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- Environment-friendly agricultural practice includes the application of pesticides when it is really necessary, e.g., at the beginning of a pest emergence. Such practice, depending on the field conditions, and the reaction of growers, for the same level of “alert”, inspired this question.Assume that in the middle of the growing season in a given area, there is one pest emergence every two weeks on average. There is a generalized emergence of pests in a given area. At this stage of the emergence, not all growers decide to apply pesticides, hoping that the emergence will be brief or without implication for their field. Accordingly, assume 75% of the growers in that area at that time decide to apply pesticides. a) What is the probability that among five growers randomly sampled, two decide not to apply pesticides? b) What is the probability that among 10 randomly sampled growers, more than nine decide to apply pesticides?Wilcoxon Signed-Rank Test The table shows the hours of relief provided by two analgesic drugs (A and B) in 12 patients suffering from arthritis. Is there any evidence that one drug provides longer relief than the other? Use alpha = 0.05. A 3.5 5.7 2.9 2.4 9.9 3.3 16.7 6.0 3.8 4.0 9.1 20.9 B 2.0 3.6 2.6 2.6 7.3 3.4 14.9 6.6 2.3 2.0 6.8 8.5A researcher designs an experiment using two drugs, she prepares 15 independent flasks of yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is provided below: Flask T Flask C Flask ND 1 8.2 6 5.2 11 6 2 6.8 7 6.1 12 5.1 3 8 8 6.2 13 5.6 4 7.6 9 5.7 14 5.2 5 7.9 10 6.3 15 6.1 a. Test if mean doubling time is different in Caffeine (C ) when compared to no drug (ND) using an ANOVA method, report an approximate p-value for the level of significance. b. If a drug decreases the doubling time of yeast cells, what could be the purpose of using this drug?
- A researcher designs an experiment using two drugs, she prepares 15 independent flasksof yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is provided below: Flask T Flask C Flask ND 1 8.2 6 5.2 11 6 2 6.8 7 6.1 12 5.1 3 8 8 6.2 13 5.6 4 7.6 9 5.7 14 5.2 5 7.9 10 6.3 15 6.1 Test if mean doubling time is different than others in at least one growth condition (ND, T or C), using a non-parametric method and report an approximate p-value for the level of significance. What is the hypotheses and the assumptions of this test?1) Malaria is a disease that destroys red blood cells (the parasite invades red blood cells, multiplies, and then infects more red blood cells). In a recent study (Kotepul, et al., 2015) looking at various blood counts, the authors found the following results. Results are in billion red blood cells / cubic mm. Note that I have deliberately modified these results (do not use R): n ̄y s Low infection 527 4.16 2.23 High infection 157 4.51 2.34 Is there a difference in red blood cell count?(Hint: please think about this before you just start working on the problem!)Activating baking yeast To shorten the time it takes him to make his favorite pizza, a student designed an experi-ment to test the effect of sugar and milk on the activation times for baking yeast. Specifically, he tested four differ-ent recipes and measured how many seconds it took for the same amount of dough to rise to the top of a bowl. Herandomized the order of the recipes and replicated eachtreatment 4 times.Here are the boxplots of activation times from the fourrecipes: The ANOVA table follows: Source DFSum ofSquaresMeanSquare F-Ratio P-ValueRecipe 3 638967.69 212989 44.7392 60.0001Error 12 57128.25 4761Total 15 696095.94 a) State the hypotheses about the recipes (both numeri-cally and in words). b) Assuming that the assumptions for inference are satis-fied, perform the hypothesis test and state your conclu-sion. Be sure to state it in terms of activation times and recipes.c) Would it be appropriate to follow up this study withmultiple comparisons to see which recipes differ…
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