It has been shown that the fertilizer magnesium ammonium phosphate, Mg4NH&PO4, is an effective supplier of the nutrients necessary for plant growth. A study was conducted at George Mason University to determine a possible optimum level of fertilization, based on the enhanced vertical growth response of the chrysanthemums. Forty chrysanthemum seedlings were divided into four groups, each containing 10 plants. Each was planted in a
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- Can attack of a plant by one organism induce resistance to subsequent attack by a different organism? In a study of this question, individually potted cotton plants were randomly allocated to two groups. Each plant in one group received an infestation of spider mites; the other group were kept as controls. After 2 weeks the mites were removed, and all plants were inoculated with a fungus that causes wilt disease. According to the research question, H0: Miles do not induce resistance to wilt. Ha: Mites do induce resistance to wilt. What is the alternative hypothesis in symbols when p represents the proportion of wilt disease in a group? p1 < p2 or p1 > p2?In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this question with the results of a statistical procedure. Use α = 0.05. Data: May= 66, June= 104, July=105, August= 88The Journal of Engineering in Industry (Aug. 1993) reported on an automated system designed to replace the cutting tool of a drilling machine at optimum times. To test the system, data were collected over a broad range of materials, drill sizes, drill speeds, and feed rates – called machining conditions. Although a total of 168 different machining conditions were possible, only eight were employed in this study. These are described below: Experiment Workpiece Drill Size (in.) 25 25 Drill Speed (грт) 1250 1800 Feed Rate Material (ipr) .011 .005 1 Cast Iron Cast Iron Steel Steel 25 25 3750 2500 .003 .003 .008 4 Steel 25 .125 .125 2500 Steel Steel 4000 4000 3000 .0065 .009 .010 Steel .125 a. Suppose one (and only one) of the 168 possible machining conditions will detect a flaw in the system. What is the probability that the experiment conducted in the study will detect the system flaw? b. Suppose the system flaw occurs when drilling steel material with a 25-inch drill size at a speed of…
- In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Part A: Does the mean E. coli contamination differ significantly among the four months? Justify your answer to this question with the result of a statistical test. Use α = 0.05. Part B:Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this…In a study, the effects of the mane of a male lion as a signal of quality to mates and rivals was explored. Four life-sized dummies of male lions provided a tool for testing female response to the unfamiliar lions whose manes varied by length (long or short) and color (blonde or dark). The female lions were observed to see whether they approached each of the four life-sized dummies. Complete parts (a) through (e) below. a. Identify the experimental units. Choose the correct answer below. The female lions The male dummies The mane colors The mane lengths Part 2 b. Identify the response variable. Choose the correct answer below. A. Whether or not (yes or no) the mane length affected how the female lions reacted to a male dummy. B. Whether or not (yes or no) the female lions approached the same dummies. C. Whether or not (yes or no) the female lions approached a male dummy. D. Whether or not…In this study, the protection of aquatic ecosystems is an important goal of Ville de Montréal. In particular, Thomas wants to see whether the contamination of creeks (ruisseaux in French) by Escherichia coli differs among the months of May, June, July, and August. Therefore, herandomly samples six creeks in different areas. For each creek, he collects water samples from May to August, and measures the amount of E. coli, expressed in colony-forming units (CFU) per 100 mL of water. For each combination of a month and a creek, he thus obtains an E. coli contamination value, i.e., 24 observations in total. A preliminary statistical analysis produces the following results. Which pairs of months show significant differences in mean E. coli contamination? Explain your reasoning and justify your answer to this question with the results of a statistical procedure. Use α = 0.05.
- To determine the effect of a growth stimulant, 24 feedlot beef cattle were randomly assigned to three groups at eight per group. Cattles in group 3 were given an injection of 10 units of a growth hormone, cattle in group 2 received an injection of 5 units, and group 1 received no injection. The cattle are of the same breed and age and were fed identically at the same location. The weight gained, in pounds, were recorded after a specified period. Cite requisites of the experimental condition in the context of the problem for the completely randomized design to be a valid design. Explain your answer.The purification of industrial waste is often a destructive process with manybeneficial components removed from the waste as part of the cleansing process. As part of some trials to reuse industrial sludge as a mulch for planting, conservation of existing nitrogen levels in the sludge is being studied. Nitrogen is used in plants to synthesize amino acids, proteins, chlorophyll, nucleic acids, and enzymes. Initial testing showed 1 kg of sludge contained 254 mg of nitrogen and after the cleaning process there were 189 mg of nitrogen left. What is the percentage reduction of nitrogen?Based on Angel et al. (2003). A fertilizer companyis trying to determine the cheapest fertilizer mix thatprovides desired amounts of nutrients. The mix ismade by combining the following fertilizers: SSA,SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage ofpotassium (K), sulfur (S), calcium (Ca), sodium (Na)and phosphorus (P) in each fertilizer is listed in the fileP06_88.xlsx. For example, a pound of SSA is 16% Kand 26% Na. The mix must contain at least 600 poundsof K, 550 pounds of S, 750 pounds of Ca, 900 poundsof Na, and 750 pounds of P. The mix cannot containboth GUR and TSP, because if both are present in themix, the affect of other fertilizers is nullified. The costper pound (in cents) of each fertilizer is listed in thesame file. Develop a linear integer model to find theminimum-cost fertilizer mixture that meets the statedchemical requirements.
- A manufacturer produces washdown motors for the food service industry. The company manufactures the motors to order by modifying a base model to meet the specifications requested by the customer. The motors are produced in a batch environment, with the batch size equal to the number ordered. The manufacturer has recently sampled 50 customer orders. The motor manufacturer would like to determine if there is a relationship between the cost of producing the order and the order size so that it could estimate the cost of producing a particular size order. (A) Use the sample data to estimate the least squares regression model. (B) Provide an interpretation of the regression coefficients. (C) Test the significance of the overall regression model using a significance level of 0.02. (D) The company has just received an order for 30 motors. Use the regression model developed in part a to estimate the cost of producing this particular order. (E) Referring to part d, what is the 95% confidence…The viruses causing problems in strawberry plants are mainly spread by one insect, the strawberry aphid. Carly believes that as aphids feed on leaves, they transmit viruses that can cause a rapid decrease in plant growth. She decides to verify whether or not the number of strawberry aphids found on a plant could be linked to its growth. She therefore randomly chooses 5 strawberry plants at the same stage of development in a virus-infested garden. For each individual plant, she first collects all the aphids present on the plant and weighs them, and then weighs the entire plant to have a measure of plant growth. She obtains the following data. (Attach on side) Is Carly correct in thinking that when the number of aphids on a plant is larger, the growth of the plant is affected (i.e., its weight is smaller)? Apply the appropriate statistical method with a test of significance at α = 0.05.In many colleges, educators are changing their approach to instruction from a “teacher/lecture-centeredmodel” to a “student-centered model” where students learn in a laboratory environment in which lectureis deemphasized and students can proceed at a pace suitable to their learning needs. In once schoolwhere this model was being introduced, of the 743 students who enrolled in the traditional lecture model, 364 passed; of the 567 in the student-centered model, 335 passed. Use a 0.05 level ofsignificance to test the claim that student-centered model results in a higher pass rate than the traditionalmodel?