Impurities in the form of iron oxides lower the economic value and usefulness of industrial minerals, such as kaolins, to ceramic and paper-processing industries. A 24 experiment was conducted to assess the effects of four factors on the percentage of iron removed from kaolin samples (“Factorial Experiments in the Development of a Kaolin Bleaching Process Using Thiourea in Sulphuric Acid Solutions,” Hydrometallurgy, 1997: 181–197). The factors and their levels are listed in the following table:
The data from an unreplicated 24 experiment is listed in the next table.
a. Calculate estimates of all main effects and two-factor interaction effects for this experiment.
b. Create a
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- The article “Effects of Diets with Whole Plant-Origin Proteins Added with Different Ratiosof Taurine:Methionine on the Growth, Macrophage Activity and Antioxidant Capacity ofRainbow Trout (Oncorhynchus mykiss) Fingerlings” (O. Hernandez, L. Hernandez, et al.,Veterinary and Animal Science, 2017:4-9) reports that a sample of 210 juvenile rainbowtrout fed a diet fortified with equal amounts of the amino acids taurine and methionine for aperiod of 70 days had a mean weight gain of 313 percent with a standard deviation of 25, while 210 fish fed with a control diet had a mean weight gain of 233 percent with a standard deviation of 19. Units are percent. Find a 99% confidence interval for the difference in weight gain on the two diets.arrow_forwardThe article "Influence of Supplemental Acetate on Bioremediation for Dissolved Polycyclic Aromatic Hydrocarbons" (T. Ebihara and P. Bishop, Journal of Environmental Engineering, 2002:505-513) describes experiments in which water containing dissolved polyaromatic hydrocarbons (PAH) was fed into sand columns. PAH concentrations were measured at various depths after 25, 45, and 90 days. Assume that three independent measurements were made at each depth at each time. The data presented in the following table are naphthalene concentrations (in mg/L) that are consistent with means and standard deviations reported in the article. 90 days 25 days 11.15 11.39 11.36 9.28 8.15 8.59 7.68 7.59 7.41 5 14.40 11.78 11.92 9.44 9.34 9.33 7.53 7.92 7.12 Depth 45 days 15 11.51 11.01 11.09 9.34 9.11 8.94 7.43 7.47 7.53 30 12.77 12.18 11.65 9.37 9.27 9.05 7.60 7.48 7.84 50 11.71 11.29 11.20 9.25 8.97 9.29 7.76 7.84 7.68 75 11.18 11.45 11.27 9.09 8.86 8.78 7.72 7.61 7.74 a Construct an ANOVA table. You may…arrow_forwardRecycling newsprint is important in reducing waste. The article "The Influence of Newspaper Aging on Optical Properties of its De-inked Pulp" (M. Rahmaninia, A. Latibari, et al., Turkish J Eng Env Sci, 2008:35-39) presents the results of an experiment to determine the effects of the age of newsprint on the brightness (in percent) of the recycled paper. Four aging periods were considered, along with five concentrations of sodium hydroxide (NaOH), used to de-ink the paper. The effect of the sodium hydroxide concentration is not of interest. The results are presented in the following table. NaOH Concentration Age (Months) 2% 0% 0.5% 1% 1.5% 54.6 54.3 55.5 56.3 56.6 4 45.6 44.1 43.7 45.6 47.1 46.1 45.9 46.4 45.0 47.9 12 44.0 44.1 45.2 43.7 46.5 a. Identify the blocking factor and the treatment factor. b. Construct an ANOVA table. You may give ranges for the P-values. Can you conclude that brightness differs with age? Explain. C. d. Which pairs of ages, if any, can you conclude to have…arrow_forward
- The vulnerability of inshore environments to contamination due to urban and industrial expansion in Mombasa is discussed in the paper “Metals, Petroleum Hydrocarbons and Organo- chlorines in Inshore Sediments and Waters on Mombasa, Kenya” [Marine Pollution Bulletin (1997) 34:570–577]. A geochemical and oceanographic survey of the inshore waters of Mombasa, Kenya, was undertaken during the period from September 1995 to January 1996. In the survey, suspended particulate matter and sediment were collected from 48 stations within Mombasa’s estuarine creeks. The concentrations of major oxides and 13 trace elements were determined for a varying number of cores at each of the stations. In particular, the lead concentrations in sus-pended particulate matter (mg kg21 dry weight) were determined at 37 stations. The researchers were interested in determining whether the average lead concentration was greater than 30 mg kg21 dry weight. The data are given in the following table along with summary…arrow_forwardThe vulnerability of inshore environments to contamination due to urban and industrial expansion in Mombasa is discussed in the paper “Metals, Petroleum Hydrocarbons and Organo- chlorines in Inshore Sediments and Waters on Mombasa, Kenya” [Marine Pollution Bulletin (1997) 34:570–577]. A geochemical and oceanographic survey of the inshore waters of Mombasa, Kenya, was undertaken during the period from September 1995 to January 1996. In the survey, suspended particulate matter and sediment were collected from 48 stations within Mombasa’s estuarine creeks. The concentrations of major oxides and 13 trace elements were determined for a varying number of cores at each of the stations. In particular, the lead concentrations in sus-pended particulate matter (mg kg21 dry weight) were determined at 37 stations. The researchers were interested in determining whether the average lead concentration was greater than 30 mg kg21 dry weight. The data are given in the following table along with summary…arrow_forwardFluoride Exposure in Drinking Water Exercise 2.250 introduces a study showing that fluoride exposure might have long-term negative consequences for the offspring of pregnant women. Part of the study examines the effect of adding fluoride to tap water on mean fluoride concentration in women. Summary statistics for fluoride concentration (measured in mg/L) for the two groups are given in the table below. Tap water Fluoridated Non-fluoridated Conclusion: Sample size 141 228 Mean 0.69 0.40 St.Dev. 0.42 0.27 Find and interpret a 99% confidence interval for the mean increase in fluoride concentration for those with fluoridated tap water. Let Group 1 represent those with fluoridated tap water and Group 2 represent those without fluoridated tap water. Confidence interval: i to i (round to three decimal places)arrow_forward
- In experiments to determine the effectiveness of drugs such as anti-fungal ointments that are applied to the skin, the concentration of the drug in a patient’s skin must be measured. The article “Determining Bioequivalence of Topical Dermatological Drug Products by Tape- Stripping” (W. Navidi, A. Hutchinson, et al., Journal of Pharmacokinetics and Pharmacodynamics, 2008:213–220) describes an improved method of measuring that is designed to ensure that all the drug in the skin is recovered. Assume that in an experiment using the old method, the mean amount of drug recovered from a sample of 49 patients was 105 ng with a standard deviation of 20 ng, and that in an experiment using the new method the mean amount of drug recovered in a sample of 35 patients was 117 ng with a standard deviation of 15 ng. Find a 98% confidence interval for the difference in the mean amounts recovered between the two methods.arrow_forward5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987) studied the impact of temperature (the regressor) on the viscosity (the response) of toluene- tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. Temperature (°C) Viscosity (mPa·s) 24.9 1.133 35.0 0.9772 44.9 0.8532 55.1 0.7550 65.2 0.6723 75.2 0.6021 85.2 0.5420 95.2 0.5074 c. Basic principles of physical chemistry suggest that the viscosity is an exponential function of the temperature. Repeat part b using the appropriate transformation based on this information.arrow_forwardThe antibiotic gentamicin sulphate is often blended with acrylic bone cement to help prevent infection following joint replacement surgery. The article "Incorporation of Large Amounts of Gentamicin Sulphate Into Acrylic Bone Cement: Effect on Handling and Mechanical Properties, Antibiotic Release, and Biofilm Formation" (N. Dunne, P. MCAfee, et al., Journal of Engineering in Medicine, 2008:355-365) presents a study of the effect of the amount of antibiotic added on various properties of the cement. Following are measurements of the setting time of the cement, for six levels of antibiotic amount, and three replications per level. The measurements are consistent with means and standard deviations presented in the article. Antibiotic per 40 g Cement Setting Time (min) 0g 0.58 1g 12.7 14.1 13.2 13.5 14.5 14.6 12.7 13.4 13.2 12.7 13.6 14.1 13.4 13.5 14.3 14.5 13.5 14.9 Construct an ANOVA table. You may give a range for the P-value. Can you conclude that there are differences among the mean…arrow_forward
- A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.4 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.2 10.9 10.6 10.6 11.9 10.1 9.9 12.3 10.7 8.8 10.2 10.4 10.3 10.9 11.4 10.4 9.3 11.6 10.6 10.9 10.9 8.3 After 9 Days Treatment Control 138.3 9.2 104 8.9 96.4 8.9 89 10.1 88 9.6 103.8 8.6 147.3 10.4 97.1 12.4 172.6 9.2 146.3 9.5 99 8.4 122.3 8.8 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if…arrow_forwardA deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.2 9.1 9.6 8.7 10.1 9.7 8.5 10.8 10.3 10.9 10.6 10.6 11.7 10.1 9.7 12.3 10.8 8.8 10.3 10.4 10.4 10.9 11.2 10.4 9.4 11.6 10.6 10.9 10.7 8.4 After 9 Days Treatment Control 138.3 9.3 104 8.7 96.4 8.7 89 10.1 88 9.6 103.8 8.6 147.3 10.2 97.1 12.2 172.6 9.3 146.3 9.5 99 8.2 122.3 8.9 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if there…arrow_forwardA deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of a research paper supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement (the treatment group) and a control sample given no supplement, both initially and after a 9-day period. Initial Measurement Treatment Control 11.3 9.1 9.7 8.7 10.1 9.7 8.5 10.8 10.4 10.9 10.7 10.6 11.8 10.1 9.8 12.3 10.6 8.8 10.4 10.4 10.2 10.9 11.3 10.4 9.2 11.6 10.7 10.9 10.8 8.2 After 9 Days Treatment Control 138.3 9.4 104 8.8 96.4 8.8 89 10.1 88 9.7 103.8 8.7 147.3 10.3 97.1 12.3 172.6 9.4 146.3 9.5 99 8.3 122.3 8.9 103 12.5 117.8 9.1 121.5 93 (a) Use the given data for the treatment group to determine if…arrow_forward
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