Problem 1 To compare the braking distance for two types of tires, a safety engineer conducts 50 braking tests for each of the two types of tires. The results of the tests are shown in the table below. Assume o, and o, are known. 2 Type C n₁ = = 50 x₁ = 55 feet 0₁ = 5.3 feet Type D n₂ = 50 X₂=51 feet 0₂ = 4.9 feet At a = 10%, can the engineer support the claim that the mean braking distance for Type C is greater than the mean breaking distance for type D?

do Q1 & Q2  which is shown in image

When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the pressure drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): 1 2 3 4 5 7 8. 9 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 | 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 (a) Fit the least square regression equation to predict the flux (flow per area) through the pressure drop across a membrane. (b) Find the estimated flux when the pressure drop across a membrane is 4.50. (c) Calculate the coefficient of correlation. Interpret your result. (d) Given Sxx = 83.25961 and Se = 0.64460653. Test, at the 0.01 level of significance, whether there is linear relationship between the pressure drop across a membrane and the flux (flow per area) through the membrane. (e) Construct a 98% confidence interval for the mean flux for the…

Q1: The data points below are related to a chemi-thermo-mechanical pulp from mixed density hardwoods. They relate Y (specific surface area of the fibres in cm/g) to the % NaOH (sodium hydroxide) used as a pretreatment chemical and the treatment time (min) for different batches of pulp. The variables are present at three different levels. In this case, it is preferred (for reasons that we will discuss later in the course) to code the levels as shown in the last two columns of the table below, designated by Xı and X2. Y SODIUM ΤΙME Xi X2 HYDROXIDE 5.95 3 30 -1 5.60 3 60 -1 5.44 3 90 -1 1 6.22 9. 30 -1 5.85 9 60 5.61 9. 90 1 8.36 15 30 1 -1 7.30 15 60 1 6.43 15 90 1 1 a. Using the variables Y, X1 and X2 (not actual time and sodium hydroxide! You will see why later!), fit the following multiple linear regression model to the data: (Model A) Y = (b0) + (b1) X1 + (b2) X2; subsequently, estimate the parameters and examine the residual plot (residuals vs Y hat). What does this residual plot…

Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at Which of the following would linearize the data for volume and time? different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved Seconds, cm3 O In(Seconds), cm3 Seconds, In(cm') pattern. O In(Seconds), In(cm³)

i am confused?

Please assist with the following questions with the answers.

For #19, where did the 2x come from?