1. As heat is added to a material its temperature rises. The heat capacity is a quantitative statement of the increase in temperature for a specified addition of heat. These data are obtained in X, the measured heat capacity of liquid ethylene glycolat constant pressure and 80 C. Measurements are in calories pergram degree Celsius: .645 .654 .640 .627 .626 .649 .629 .631 .643 .633 .646 .630 .634 .631 .651 .659 .638 .645 .655 .624 %D .658 .658 .658 .647 .665
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- An article in the ASCE Journal of Energy Engineering [“Overview of Reservoir Release Improvements at 20 TVA Dams” (Vol. 125, April 1999, pp. 1–17)] presents data on dissolved oxygen concentrations in streams below 20 dams in the Tennessee Valley Authority system. The observations are (in milligrams per liter):A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40°C. Round the answers to three decimal places. The 95% prediction interval is ( , ).A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Compute the error variance estimate s2. Round the answer to three decimal places.
- A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.5x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.5 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find 95% confidence intervals for β0 and β1. Round the answers to three decimal places. The 95% confidence interval for β0 is ( , ). The 95% confidence interval for β1 is ( , ).) The following table shows 10 communities ranked by decayed, missing, or filled (DMF) teeth per 100 children and fluoride concentration in ppm in the public water supply: Rank by DMF Teeth FluorideCommunity per 100 children X Concentration Y 1 8 1 2 9 3 3 7 4 4 3 9 5 2 8 6 4 77 1…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?
- The data given below indicate the existence of a linear relationship between the x and y variables. Suppose an analyst who prepared the solutions and carried out the RI measurements was not skilled and as a result of poor technique, allowed intermediate errors to appear. The results are the following:Concentration of solution in percent (x) 10 26 33 50 61Refractive indices (y) 1.497 1.493 1.485 1.478 1.477Step 1. Carefully plot the given x and y values (from the table) on a regular graphing paper. Label then connect the points to observe a zigzag plot due to the scattered points. Step 2: Copy and fill the table given below: x (x - x̄) (x - x̄) 2 y (y - ȳ) (y - ȳ) 2 (x - x̄) (y - ȳ) 10 1.497 26 1.49333 1.48550 1.47861 1.477∑ = ∑ = ∑ = ∑ = ∑ = ∑ = ∑ =x̄= ∑xi ÷ Nx̄= ȳ = ∑yi ÷ Nȳ = Step 3. After completing the table, present following computations and the interpretation.a. Calculate the correlation coefficient (r), using the working formula: r =Σ (x − x ) (y − ȳ)√(Σ(x − x )2)(Σ(y −…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≤In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in °C and evaporation in millimetres per day were taken for 10 days. The results are shown in the following table. Temperature Evaporation 11.9 2.4 21.5 4.8 16.5 5.0 23.6 4.1 19.1 6.2 21.6 5.9 31.3 4.8 18.9 3.0 24.2 7.3 19.3 1.6 Test H0: β1 = 0 versus H1: β1 ≠ 0. Can you conclude that temperature is useful in predicting evaporation? Use the α = 0.01 level of significance.
- 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≤blankSuppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8, x = 114.6, s1 = 5.03, n = 8, y = 129.3, and s2 = 5.38. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) ,Consider the following data relating hours spent studying (X) and average grade on course quizzes (Y): X Y 5 6 3 8 4 8 7 10 5 7 6 9 Compute SP (equation below) 420 5 6 17
