Concept explainers
The accompanying summary quantities for x = Particulate pollution (μg/m3) and y = Luminance (0.01 cd/m2) were calculated from a representative sample of data that appeared in the article “Luminance and Polarization of the Sky Light at Seville (Spain) Measured in White Light” (Atmospheric Environment [1988]: 595–599).
- a. Test to see whether there is a
positive correlation between particulate pollution and luminance in the population from which the data were selected. - b. What proportion of observed variation in luminance can be attributed to the approximate linear relationship between luminance and particulate pollution?
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INTRODUCTION TO STATISTICS & DATA ANALYS
- The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where w is the crack width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w = 1.2 ± 0.1 mm.a) Estimate v, and find the uncertainty in the estimate.b) Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?arrow_forwardIn trying to minimise errors that come with using a tape in linear measurements, Mapalo suggested to the class that an EDM be used to compute the distance from BM1 to point A. A distance of 2122.241m was measured. Given that a frequency of 1.4985MHz was used, speed of light c = 299792458m/s, the refraction index of 1.0003 and that the effective wavelength measures to a centimetre, determine the phase measurement (i.e. Phase Distance and the corresponding Phase angle)arrow_forwardAs an industrial engineer is working a test of material used to on a certain product to determine whether it is more economical to repair a damaged area rather than replace the entire structure. The engineer obtained the following data on the bond length (x variable) vs. the rupture load (y variable) Bond Length (mm) Rupture Load (N) 50 17,052 50 14,063 80 26,264 80 19,600 110 21,952 110 26,362 140 26,362 140 26,754 170 31,654 170 32,928 Find the 95% Confidence Interval for the conditional mean of the response variable at x = 140arrow_forward
- If I have 2 for the degrees of freedom with an alpha of 0.05, what would be the critical value of t?arrow_forwardFind the critical values of Z for a two tail test at alpha α = 0.01 LOS.arrow_forwardLet yt = φyt−1 + et with et ∼ WN(0,σ2) and |φ| < 1. Consider the over-differenced process wt = (1 − L)yt.(i) What is the model followed by wt? (ii) Is wt invertible? (iii) Obtain V [wt] and compare its magnitude with V [yt] and hence comment on the impact of over-differencing on the variance of a stationary process.arrow_forward
- Can you find the amount of salt A in the tank at any time t?arrow_forwardThe thermal conductivity (R-Value) of 23 samples of newly developed inulating material follows: 4.626 4.755 4.596 4.398 4.497 4.833 4.866 4.398 4.638 4.482 4.644 4.878 4.32 4.824 4.56 4.434 4.626 4.533 4.377 4.599 4.596 4.569 4.191 Which of the following equations should be used in to find a 95% one-sided lower CI on the mean thermal conductivity.arrow_forwardWhat is the value of the beta function, B(x, y), where x and y are positive real numbers?arrow_forward
- In the article “Influence of Crack Width on Shear Behaviour of SIFCON” (C. Fritz and H. Reinhardt, High Performance Fiber Reinforced Cement Composites: Proceedings of the International RILEM/ACI Workshop, 1992), the maximum shear stress τ of a cracked concrete member is given to be τ = τ0(1 − kw), where τ0 is the maximum shear stress for a crack width of zero, w is the crack width in mm, and k is a constant estimated from experimental data. Assume k = 0.29 ± 0.05 mm−1. Given that τ0 = 50 MPa and w = 1.0 mm, both with negligible uncertainty, estimate τ and find the uncertainty in the estimate.arrow_forwardRestate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water level rises at a rate of 1 cm/min?arrow_forwardIs there a way to solve this w/o using L'Hospital's rule?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage