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- Refer to Exercise 7. Assume that p = 4.3 ± 0.1 cm and q = 2.1 ± 0.2 cm. Estimate f, and find the relative uncertainty in the estimate.Refer to Exercise 8.a) Assume that P = 224.51 ± 0.04 kPa and V = 11.237 ± 0.002 L. Estimate T, and find the relative uncertainty in the estimate.b) Assume that P = 224.51 ± 0.04 kPa and T = 289.33 ± 0.02 K. Estimate V, and find the relative uncertainty in the estimate.c) Assume that V = 11.203 ± 0.002 L and T = 289.33 ± 0.02 K. Estimate P, and find the relative uncertainty in the estimate.A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) 3 3.5 4 5 6 6.5 7 8 8.5 9 9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 (i) Draw a scatter diagram. (ii) Calculate the product moment correlation coefficient and comment on your answer. (iii) Construct the least squares regression line.
- The average normal daily temperature ( in degree Celsius) and the corresponding average monthly precipitation( in inches ) for the month of June are shown below for seven randomly selected cities. Compute for the value of r, complete the table with the needed information. Temperature(x) 30 27 28 32 27 23 18 Precipitation(y) 3.4 1.8 3.5 3.6 3.7 1.5 0.2In a survey that included assessment of husband-and-wife heights, Hodges, Krech, and Crutchfield (1975) reported the following results. Let’s treat wife height as the predictor (X) variable and husband height as the outcome (Y) variable: rXY=.32 Wifeheight: MX=64.42, sX=2.56 Husbandheight: MY=70.46, sY=2.87 N=1,296 Calculate the values of the b0 and b coefficients to predict husband height in inches (Y) from wife height in inches (X) and write out this raw-score predictive equation. For a woman who is 62 in. tall, what is the predicted height of her future husband (on the basis of your equation for part a)? If her husband’s actual height turns out to be 73 in., what can you say about the difference between predicted and actual height? Do some short women marry tall men? Would the equation to predict wife height from husband height be the same as your equation in part a? Why or why not? What proportion of variance in husband height is predictable from wife height? What proportion of…A farmer would like to investigate the relationship between the obtained yield of apple trees and the amount of weeds found in their roots. For this reason, nine apple trees of the same type were randomly selected and the amount of weeds in their roots (x grams) was recorded together with their yield (y kilograms). Year #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Weeds in roots (x) 30 28 32 25 25 24 22 24 35 40 Yield (y) 25 30 27 40 42 41 50 45 30 25 Draw a scatter diagram of these data. Label the diagram carefully. Calculate the sample correlation coefficient. Interpret your findings. Calculate the least squares line of y on x and draw the line on the scatter diagram. Based on the regression equation in part (iii.), what will be the predicted yield of apple for a tree with 37 grams of weeds in its roots? Will you trust this value? Justify your answer. Briefly comment on…
- 2- An expert estimates that the distribution parameter for durability times of parts produced with machine A in the factory is different from the distribution parameter for durability times of parts produced with machine B. Durability times of 4 parts produced from machine A and 4 parts produced from machine B are given below. Find the Mann-Whitney U value by using these data. a) 18 B) 6 NS) 16 D) 20 TO) 12Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 6 10 13 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.. 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.
- 3. Draw a picture that shows the difference between dy and ∆y.The amount of time a student devotes to class attendance and revision: and the grade obtained are assumed to be linearly related. In a small class of 15 students, the following results were obtained for this linear relationship. Y = 30 +2.50.Y (0.55) (2.96) R'= 0.85 The standard errors are in parenthesis. a,Test the hypothesis that the intereept and slope are individually equal to zero (0) at the S% level of signiticance. (b) Construct n 95% conlidence interval for the true slope. (c)Compute the elasticity of grades with respect to time input and interpret your results. (d) Interpret your R' and explain how it relates to the slope of the regression line. (e) From the results and your answers in (a) to (d), does time input into class attendance and revision really influence the final grade?The length of North Sea sole, a species of fish, can be determined using the von Bertalanffy model given below. L = 14.8 − 19.106 × 0.631t At what year will the sole be 7 inches long?