Water Quality. In the article “Randomized Stratified Sampling Methodology for Water Quality in Distribution Systems” (Journal of Water Resources Planning and Management, Vol. 130, Issue 4, pp. 330–338), V. Speight et al. proposed the method of stratified sampling to collect water samples for water-quality testing. The following table separates the Durham, North Carolina water distribution system into strata based on distance from the nearest treatment plant.
Distance from treatment center | Stratum size |
Less than 1.5 miles | 1310 |
1.5–less than 3.0 miles | 3166 |
3.0–less than 4.5 miles | 2825 |
4.5–less than 6.0 miles | 1593 |
6.0–less than 7.5 miles | 1350 |
7.5 miles or greater | 1463 |
Use the table to design a procedure for obtaining a stratified sample (with proportional allocation) of 80 water samples from Durham.
Hint: Refer to the remarks about strata
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Introductory Statistics, Books a la Carte Plus NEW MyLab Statistics with Pearson eText -- Access Card Package (10th Edition)
- b) The data in table 4b below gives the number of nonconforming bearings and seal assemblies in a sample size of 100. Sample No. Nonconforming Assemblies i. iii. 1 2 3 4 5 6 6523 7 8 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10 5 3 7 6 16 0981415710 Table 4b Calculate the UCL and LCL for this data Plot a fraction non-conforming control chart for the data. If any points plot outside of the control limits, assume that assignable causes can be found and determine the revised control limits.arrow_forward2. Data on speed versus fuel consumption for two automobiles are: Sample Number Speed For Car Fuel For Car #1 Fuel For Car # 2 #1 & 2 (mi/ hr) 1 100 5 10 2 90 10 18 3 80 15 20 4 70 20 25 60 22 30 6 50 24 35 7 40 26 40 8. 30 28 43 20 30 42 Prepare a scatter diagram and analyze the results.arrow_forwarda. Graphic image of basic material grain analysis; b. Create a parameter table for the grain size frequency distribution of the basic material in mm and , for the grain size frequency distribution parameters d5, d16, d25, d50, d75, d84, d95; c. Determine the basic material statistical parameters, namely mean, sorting, skewness, and kurtosis on Krasak 1, 2, and 3. Complete with classification and descriptionsarrow_forward
- QUESTION 1 A quality engineer has measured the size of the component produced by the production department. The sizes of the component is recorded and distributed as in Table 1. You as the engineer are assigned to study the quality of the component produced from the production line. a) Construct the histogram. b) Estimate the skewness, kurtosis and coefficient of variation. c) What is your judgement concerning the normality of the distribution? Table 1 1.5 1.2 3.1 1.3 0.7 1.3 0.1 2.9 1.0 1.3 2.6 1.7 0.3 0.7 2.4 1.5 0.7 2.1 3.5 1.1 0.7 0.5 1.6 1.4 1.7 3.2 3.0 1.7 2.8 2.2 1.8 2.3 3.3 3.1 3.3 2.9 2.2 1.2 1.3 1.4 2.3 2.5 3.1 2.1 3.5 1.4 2.8 2.8 1.5 1.9 2.0 3.0 0.9 3.1 1.9 1.7 1.5 3.0 2.6 1.0 2.9 1.8 1.4 1.4 3.3 2.4 1.8 2.1 1.6 0.9 2.1 1.5arrow_forward3. A study was carried out into the attendance rate at a hospital of people in 16 different geographical areas, over a fixed period of time. The distance of the centre from the hospital of each area was measured in miles. The results were as follows: (1) 21%, 6.8; (2) 12%, 10.3; (3) 30%, 1.7; (4) 8%, 14.2; (5) 10%, 8.8; (6) 26%, 5.8; (7) 42%, 2.1; (8) 31%, 3.3; (9) 21%, 4.3; (10) 15%, 9.0; (11) 19%, 3.2; (12) 6%, 12.7; (13) 18%, 8.2; (14) 12%, 7.0; (15) 23%, 5.1; (16) 34%, 4.1. a. What is the correlation coefficient (Pearson Product Moment Correlation) between the attendance rate and mean distance of the geographical area? b. Find the Spearman rank correlation for the data givenarrow_forward1.) Standing eye heights of women are normally distributed with a mean of 1516 mm and a standarddeviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.).a.) A door peephole is placed at a height that is uncomfortable for women with standing eye heightsgreater than 1605 mm. What percentage of women will find that height uncomfortable?b.) In selecting the height of a new door peephole, the architect wants its height to be suitable for thehighest 99% of standing eye heights for women. What standing eye height of women separates thehighest 99% from the lowest 1%?c.) What percentage of women have a standing eye height between 1420 mm and 1560 mm?d.) What is the probability that a group of twenty women have an average standing eye height that isless than 1500 mm? Even though our sample size is less than thirty, why can the Central Limit Theoremstill apply here?arrow_forward
- 5. To compare the wearing qualities of two types of automobile tires, A and B, a tire of type A and one of type Bare randomly assigned and mounted on the rear wheels of each of five automobiles. The automobiles are then operated for a specified number of kilometers, and the amount of wear is recorded for each tire. These measurements appear in the following table. We wish to find sufficient evidence to indicate a difference in the average wear for the two tire types. Use a 10% level of significance for the following three methods: Tire A Automobile Tire B 1. 10.6 10.2 9.8 9.4 3 12.3 11.8 4 9.7 9.1 5 8.8 8.3 a) Use the sign test. b) Use the t-test for independent small samples. c) Use the t-test for dependent small samples.arrow_forwardSamples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table. 2. 3. 6. Location Surface pH 6.55 5.98 5.59 6.17 5.92 6.18 6.43 5.68 Subsoil pH 6.78 6.14 5.80 5.91 6.10 6.01 6.18 5.88 a. Compute a 90% confidence interval for the mean differend between surface and subsoil pH for agricultural land in this county. b. What assumptions are necessary for the interval in Part (a) to be valid?arrow_forward4. Medicinal value of plants. Sea buckthorn (Hippophae), a plant that typically grows at high altitudes in Europe and Asia, has been found to have medicinal value. The medicinal properties of berries collected from sea buckthorn were investigated in Academia Journal of Medicinal Plants (Aug. 2013). The following variables were measured for each plant sampled. Identify each as producing quantitative or qualitative data. Species of sea buckthorn (H. rhamnoides, H. gyantsensis, H. neurocarpa, H. tibetana, or H. salicifolia) Altitude of collection location (meters) Total flavonoid content in berries (milligrams per gram) а. b. с.arrow_forward
- A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer. Color Texture Light Medium Dark Fine 7 15 4 Medium 5 18 15 Coarse 17 29 5arrow_forwardRead this sample from the report. “In March 2015, 61 percent of workers in private industry had paid sick leave benefits. About 7 in 10 of those workers received a fixed number of sick leave days each year. Among those who received a fixed number of sick leave days, the amount varied depending on the employee’s length of service and the size of the establishment.” Question Q. According to the chart, the “All Establishments” category appears to fall in the middle of the data points when compared to the other categories. What could be the reason for this? A.The “All Establishments” category is an average of the data from the other categories. B.The “All Establishments” category represents industries that were not surveyed for the report. C.The “All Establishments” category predicts what paid sick days will be in the future.arrow_forwardSeveral methods of estimating the number of seeds in soil samples have been developed by ecologists. An article gave the accompanying data on the number of seeds detected by the direct method and by the stratified method for 27 soil specimens. Specimen Direct Stratified 1 21 7 2 34 38 3 0 7 4 60 58 5 20 54 6 61 61 7 40 27 8 7 7 9 14 7 10 94 100 11 1 0 12 67 58 13 78 67 14 21 54 Specimen Direct Stratified 15 34 27 16 0 0 17 38 38 18 18 14 19 94 94 20 1 14 21 40 47 22 21 21 23 0 0 24 7 14 25 14 40 26 18 14 27 40 78 Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using ? = 0.05. (Use ?direct − ?stratified.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill