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- The determination of the shear strength of spot welds is relatively difficult, whereas measuring the weld diameter of spot welds is relatively simple. As a result, it would be advantageous if shear strength could be predicted from a measurement of weld diameter. The data are as follows: Shear strength (psi) Weld diameter (0.0001 in) 370 400 780 800 1210 1250 1560 1600 1980 2000 2450 2500 3070 3100 3550 3600 3940 4000 3950 4000 a) Test the hypothesis that the slope of the regression line is equal to 1 at the 0.05 level of significance.Periodically, the county Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below. lead (μμg/L) copper (mg/L) 4.4 0.643 2.4 0.57 1.5 0.46 2.6 0.895 5.9 0.2 3.4 0.54 3.8 0.245 1.6 0.583 5.7 0.769 1.7 0.215 (a) Construct a 9999% confidence interval for the mean lead level in water specimans of the subdevelopment. ≤μ≤The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.
- The vapor pressure of 1-chlorotetradecane at several temperatures are tabulated below. T (ºC) P∗ mm Hg 98.5 1 131.8 5 148.2 10 166.2 20 199.8 60 215.5 100 What error is there in using two-point linear interpolation to find the value of vapor pressure at 185ºC?Periodically, the county Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below. lead (μμg/L) copper (mg/L) 4.44.4 0.6430.643 2.42.4 0.570.57 1.51.5 0.460.46 2.62.6 0.8950.895 5.95.9 0.20.2 3.43.4 0.540.54 3.83.8 0.2450.245 1.61.6 0.5830.583 5.75.7 0.7690.769 1.71.7 0.2150.215 (a) Construct a 9999% confidence interval for the mean lead level in water specimans of the subdevelopment. ≤μ≤≤μ≤ (b) Construct a 9999% confidence interval for the mean copper level in water specimans of the subdevelopment. ≤μ≤≤μ≤An article in the Journal of Applied Polymer Science (Vol. 56, pp. 471–476, 1995) studied the effect of the mole ratio of sebacic acid on the intrinsic viscosity of copolyesters.- The data follows: Viscosity 0.45 0.2 0.34 0.58 0.7 0.57 0.55 0.44 Mole ratio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (a) Construct a scatter diagram of the data.
- How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures, in degrees Celsius, and mean coral growth, in centimeters per year, over a several‑year period at locations in the Gulf of Mexico and the Caribbean Sea. The table shows the data for the Gulf of Mexico. Sea surface temperature 26.726.7 26.626.6 26.626.6 26.526.5 26.326.3 26.126.1 Growth 0.850.85 0.850.85 0.790.79 0.860.86 0.890.89 0.920.92 (b) Find the correlation ?r step by step. Round off to two decimals places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for ?r . Round your answer to three decimal places.The following data pertain to x, the amount of fertil-izer (in pounds) that a farmer applies to his soil, and y, his yield of wheat (in bushels per acre): xy xy xy112 33 88 24 37 2792 28 44 17 23 972 38 132 36 77 3266 17 23 14 142 38112 35 57 25 37 1388 31 111 40 127 2342 8 69 29 88 31126 37 19 12 48 3772 32 103 27 61 2552 20 141 40 71 1428 17 77 26 113 26 Assuming that the data can be looked upon as a randomsample from a bivariate normal population, calculate rand test its significance at the 0.01 level of significance.Also, draw a scattergram of these paired data and judgewhether the assumption seems reasonable.The article “Effect of Internal Gas Pressure on the Com- pression Strength of Beverage Cans and Plastic Bottles” (J. of Testing and Evaluation, 1993: 129–131) includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. What assumptions are necessary for your analysis? ( use ? = 0.01 )
- The owner of a new car conducts a series of six gas mileage tests and obtains the following results, expressed in miles per gallon: 3., 22.7, 21.4, 20.6, and 21.4. 20.9. Find the mode for these data.Periodically, the county Water Department tests the drinking water of homeowners for contminants such as lead and copper. The lead and copper levels in water specimens collected in 1998 for a sample of 10 residents of a subdevelopement of the county are shown below. lead (μμg/L) copper (mg/L) 4.44.4 0.4840.484 2.72.7 0.0760.076 5.35.3 0.5950.595 3.33.3 0.1280.128 5.55.5 0.4690.469 1.71.7 0.4060.406 0.40.4 0.8480.848 0.70.7 0.0220.022 44 0.860.86 2.82.8 0.4250.425 (a) Construct a 99% confidence interval for the mean lead level in water specimans of the subdevelopment. blank≤μ≤blank (b) Construct a 99% confidence interval for the mean copper level in water specimans of the subdevelopment. blank≤μ≤blank. Two soft drink dispensing machines should dispense 8 oz of your selection into a cup. The table below shows the data Machine 1 9.52 6.41 10.07 5.85 8.15 Machine 2 8.01 7.99 7.95 8.03 8.02 Which is more consistent in dispensing soda base on the measures of dispersion? Show all solutions.