High concentration of the toxic element arsenic is all too common in groundwater. The article “Evaluation of Treatment Systems for the Removal of Arsenic from Groundwater” (Practice Periodical of Hazardous, Toxic, and Radioactive Waste Mgmt., 2005: 152–157) reported that for a sample of n = 5 water specimens selected for treatment by coagulation, the sample
- a. Calculate and interpret a 95% CI for true average arsenic concentration in all such water specimens.
- b. Calculate a 90% upper confidence bound for the standard deviation of the arsenic concentration distribution.
- c. Predict the arsenic concentration for a single water specimen in a way that conveys information about precision and reliability.
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Chapter 7 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- The paper "Trends in Blood Lead Levels and Blood Lead Testing among U.S. Children Aged 1 to 5 Years"t gave data on blood lead levels (in mg/dL) for samples of children living in homes that had been classified either at low, medium, or high risk of lead exposure, based on when the home was constructed. After using a multiple comparison procedure, the authors reported the following. 1. The difference in mean blood lead level between low-risk housing and medium-risk housing was significant. 2. The difference in mean blood lead level between low-risk housing and high-risk housing was significant. 3. The difference in mean blood lead level between medium-risk housing and high-risk housing was significant. Which of the following sets of T-K intervals (Set 1, 2, or 3) is consistent with the authors' conclusions? Explain your choice. • 4, = mean blood lead level for children living in low-risk housing uM = mean blood lead level for children living in mediumrisk housing Hy = mean blood lead…arrow_forwarda) Soil has been improved to increase the strength of a ground. The average compressive strength of 61 samples before treatment is 45 kg / cm2 and the standard deviation is 6.75 kg / cm2; The average compressive strength of 56 samples after the improvement is 52.5 kg / cm2 and the standard deviation is 8 kg / cm2. Determine whether the improvement application changes the standard deviation of the soil strength or not at the 5% significance level (15 P). b) Find the confidence intervals at the 7% significance level of the mean compressive strength of the sample after improvement?arrow_forwardArsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed with a mean of 3.2 mg/dl. Some areas of the United States have naturally elevated arsenic levels in the ground and water supplies. Researchers took a sample 20 water samples from a particular area and measured the arsenic levels in each of the 20 water samples. They want to determine if there is sufficient evidence to conclude that the arsenic level in that area is higher than 3.2 mg/dl. hypothesis test for one population mean (unknown population standard deviation) confidence interval estimate for one population mean (unknown population standard deviation) hypothesis test for population mean from paired differences confidence interval estimate for population mean from paired differences hypothesis test for difference in population means from two independent samples confidence interval estimate for difference in population means from two…arrow_forward
- In a test of the effectiveness of garlic for lowering cholesterol, 41 senior citizens were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol (in mg/dL) have an average (mean) of 3.8. Identify the sample, the population, the sample statistic, and the population parameter in this study.arrow_forward4. A study by Bechtel et al., 2009, described in the Archives of Environmental & Occupational Health considered polycyclic aromatic hydrocarbons and immune system function in beef cattle. Some cattle were near major oil- and gas-producing areas of western Canada. The mean monthly exposure to PM1.0 (particulate matter that is < 1µm in diameter) was approximately 7.1 ug/m3 with standard deviation 1.3. Assume that the monthly exposure is normally distributed. NOTE: Draw the standard normal curve for each item below. a. What is the probability of a monthly exposure between 4 and 6 ug/m? b. What is the probability of a monthly exposure thatis at least 7.3 ug/m³ c. What is the probability of a monthly exposure that is less than 6.9 µg/marrow_forwardThe article "Impact of Free Calcium Oxide Content of Fly Ash on Dust and Sulfur Dioxide Emissions in a Lignite-Fired Power Plant" (D. Sotiropoulos, A. Georgakopoulos, and N. Kolovos, Journal of Air and Waste Management, 2005:1042-1049) presents measurements of dust emissions, in mg/m?, for four power plants. Thirty measurements were taken for each plant. The sample means and standard deviations are presented in the following table: Mean Standard Deviation Sample Size Plant 1 211.50 24.85 30 Plant 2 214.00 35.26 30 Plant 3 211.75 33.53 30 Plant 4 236.08 23.09 30 Construct an ANOVA table. You may give a range for the P-value. Can you conclude that there are differences among the mean emission levels? a. b.arrow_forward
- Does chronic hepatitis C infection impact bone mineral density? In the general population of healthy young adults, bone mineral density is Normally distributed, and density scores are standardized to have a mean u of 0 and a standard deviation o of 1. A study examined the bone densities of a random sample of 28 adult men suffering from chronic hepatitis C infection. Their mean standardized bone density was -0.61. Does this provide strong evidence that the mean standardized bone density of adult men suffering from chronic hepatitis C infection is less than 0?arrow_forwardThe authors of the paper "Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner Store Purchases After an Environmental Intervention"† wondered if increasing the availability of healthy food options would also increase the amount people spend at the corner store. They collected data from a representative sample of 5,949 purchases at corner stores in Philadelphia after the stores increased their healthy food options. The sample mean amount spent for this sample of purchases was $2.86 and the sample standard deviation was $5.40. Find the test statistic and P-value.arrow_forwardIn a machining process, diameter of a product is of concern as a quality characteristic. Control charts are to be constructed to control the mean diameter quality characteristic. Suppose that the machining process operates with a mean diameter of 5.00 mm and a known standard deviation of o=0.09 mm. Samples of size n=9 parts will be used for the control process. a) Determine the Upper and Lower Control Limits (UCL and LCL) for the 30 control chart to be used to control mean diameter based on the sample means. UCL= LCL= b) Suppose 7 samples (each with size n=9) are taken from the process and their mean values determined as below. Indicate the sample mean which is out of control. ₁5.01, 4.90, 4.96, 5.05, 4.89, 5.095, 4.965 Sample means out of Control- Type of Error= c) If a sample mean of 5.11 is obtained and found that it is outside the control limits, the process will be stopped for corrective action because the control chart signals that the process is out of control, while the process…arrow_forward
- The valve pressure was tested on 250 engines and the mean pressure was 5.9 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 5.8 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs about the specifications?arrow_forwardIs the data accurate (mean = 97% of true value or 2% error) or precise (sd < 0.1)? If not, give ONE possible source of error.arrow_forwardSuppose that measurements of cholesterol level in women in the U.S. population aged 21-40 is normally distributed with mean 51 mg/dL. It is desired to test if the cholesterol level among Asian immigrants is different from those in the general U.S. population. A study on a sample of 120 Asian women of age 21-40 yielded an average measurement of 51.91 with a standard deviation of 5. The appropriate formulation of the testing problem is. Ho : μ 51 Ho = 51,H₁ : μ #51 μ Ho : μ > 51 ,Η : μ < 51 Submit Answer Tries 0/3 Refer to the previous probelm. What is the p-value of the observations? 0.0462 0.0231 0.9538 Submit Answer Tries 0/3 Refer to the previous problems. If a =0.0762, what is your conclusion for the test? do not reject Ho reject Hoarrow_forward
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