Solid copper produced by sintering (heating without melting) a powder under specified environmental conditions is then measured for porosity (the volume fraction due to voids) in a laboratory. A sample of n1 = 4 independent porosity measurements have mean
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Mathematical Statistics with Applications
- Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"+ investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. USE SALT (a) What is the probability that the size of a single droplet is less than 1380 µm? At least 950 µm? (Round your answers to four decimal places.) less than 1380 μm at least 950 μm (b) What is the probability that the size of a single droplet is between 950 and 1380 µm? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest 2% of…arrow_forwardSpray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"+ investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 μm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. USE SALT (a) What is the probability that the size of a single droplet is less than 1440 µm? At least 975 μm? (Round your answers to four decimal places.) less than 1440 μm 9990 X at least 975 μm (b) What is the probability that the size of a single droplet is between 975 and 1440 µm? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest…arrow_forwardSpray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"t investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. n USE SALT (a) What is the probability that the size of a single droplet is less than 1455 µm? At least 925 um? (Round your answers to four decimal places.) less than 1455 um at least 925 um (b) What is the probability that the size of a single droplet is between 925 and 1455 um? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest 2% of…arrow_forward
- In a Ni-Cd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states. Assume the following proportions of the states: Nickel Charge Proportions Found 0 0.17 +2 0.33 +3 0.33 +4 0.5-0.33 Determine the variance of the nickel charge. Please enter the answer to 3 decimal places.arrow_forwardSpray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"† investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. (a) What is the probability that the size of a single droplet is less than 1455 µm? At least 900 µm? (Round your answers to four decimal places.) less than 1455 µm at least 900 µm (b) What is the probability that the size of a single droplet is between 900 and 1455 µm? (Round your answer to four decimal places.)(c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The…arrow_forwardThe accompanying summary quantities for x = Particulate pollution (pg/m³) and y = Luminance (0.01 cd/m2) were calculated from a representative sample of data that appeared in a article. n = 15 Ex = 870 Ey = 349 Ex? = 56,300 Ey? = 8,953 Exy = 22,215 (a) Test to see whether there is a positive correlation between particulate pollution and luminance in the population from which the data were selected. (Use a = 0.05.) Calculate the test statistic. (Round your answer to two decimal places.) t = What is the P-value? (Use technology to calculate the P-value. Round your answer to three decimal places.) P-value = What can you conclude? O Fail to reject H. We have convincing evidence of a positive correlation between particulate pollution and luminance for the population from which the sample was selected. Reject Ho. We have convincing evidence of a positive correlation between particulate pollution and luminance for the population from which the sample was selected. O Reject H.. We do not have…arrow_forward
- Mm3arrow_forwardUnfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.0 ppb arsenic, with s = 2.3 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О но: и 3 8 рb; н,: и +8 ppb O Ho: H > 8 ppb; H: µ = 8 ppb O Ho: H = 8 ppb; H: µ > 8 ppb O Ho: H = 8 ppb; H,: µ < 8 ppb O Ho: H < 8 ppb; H,: µ = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and o is unknown. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is…arrow_forwardUnfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 8 pb О Но: и> 8 рpb; Hi: и %3D 8 рpb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is unknown. What is the value of the sample test…arrow_forward
- Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of μ=8 parts per billion (ppb) is considered safe for agricultural use. A well in Los Banos is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of x=7.3 ppb arsenic. It is known that σ=1.9 ppb for this type of data. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use the classical approach. Use α=0.01 What is the hypotheses for this problem? A: Ho μ =7.3ppb vs HA μ < 7.3ppb B: Ho μ <7.3ppb vs HA μ ≥ 7.3ppb C: Ho μ =8.0ppb vs HA μ < 8.0ppb D: Ho μ <8.0ppb vs HA μ ≥ 8.0ppbarrow_forwardAn article compared the dielectric constants between two types of asphalt, HL3 and HL8, commonly used in pavements. For 42 specimens of HL3 asphalt the average dielectric constant was 5.92 with a standard deviation of 0.15, and for 37 specimens of HL8 asphalt the average dielectric constant was 6.05 with a standard deviation of 0.16. Can you conclude that the mean dielectric constant differs between the two types of asphalt? Find the P-value and state a conclusion. The P-value is . Round the answer to four decimal places. We (Click to select) cannot can conclude that the mean dielectric constant differs between the two types of asphalt.arrow_forwardThe Precision Machining Company makes hand-held tools on an assembly line that produces one product every minute. On one of the products, the critical quality dimension is the diameter (measured in thousandths of an inch) of a hole bored in one of the assemblies. Management wants to detect any shift in the process average diameter from 0.010 in. Management considers the variance in the process to be in control. Historically, the average range has been 0.002 in., regardless of the process average. Design an x-chart to control this process, with a center line at 0.010 in. and the control limits set at three sigmas from the center line. Management provided the results of 80 minutes of output from the production line, as shown in the table below. During these 80 minutes, the process average changed once. All measurements are in thousandths of an inch. Sample data for Precision Machining Company Diameter (thousandths of an inch) Minutes 1- 12 10 11 13 11 12 10 9. 8 11 12 13 - 24 10 11 12 11…arrow_forward
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