Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data301.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. (Round your answers to three decimal places.)

time    length
10      1.7
20      3.8
30      5.2
40      7.6
50      8.4
60      9.9
70      10.1
80      9.4
90      12.4
100     17.5
110     16.4
120     19.3
130     22.5
140     23.5
150     25.8
160     26.7
170     28.8
180     29.8

The data in the table is the number of absences for 7 students and their corresponding grade. Number of Absences 2 3 3 5 5 6 6 Grade 3.8 3.6 3.2 2.5 2.1 2 1.7 Table

Step 1 of 5 : Calculate the sum of squared errors (SSE). Use the values b0=4.8669 and b1=−0.5056 for the calculations. Round your answer to three decimal places.

Step 2 of 5 : Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

Step 3 of 5 : Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

Step 4 of 5 : Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

Step 5 of 5 : Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Emerald^® Designer Edition^TM is Sherwin Williams’ “finest interior architectural coating” (or, more commonly, paint). Drying time is stated to be temperature and humidity dependent: for recoating: 4 hours, assuming 77^o F and 50% relative humidity.

A contractor records relative humidity and drying time for ten recent jobs as shown at right.

1. Based on the relative humidity, what is the least squares regression equation for the drying time for this paint?
2. What percentage of the variation in drying time is explained by variation in relative humidity?
3. Using your least squares estimator, what drying time would you expect on a day with 65% relative humidity?

Emerald^® Designer Edition^TM is Sherwin Williams’ “finest interior architectural coating” (or, more commonly, paint). Drying time is stated to be temperature and humidity dependent: for recoating: 4 hours, assuming 77^o F and 50% relative humidity.

A contractor records relative humidity and drying time for ten recent jobs as shown at right.

1. Based on the relative humidity, what is the least squares regression equation for the drying time for this paint?
2. What percentage of the variation in drying time is explained by variation in relative humidity?
3. Using your least squares estimator, what drying time would you expect on a day with 65% relative humidity?

A liquid food(viscosty: 0.003 Pa S; density:1033 kg/m^3) is being pumped at a rate of 3 m^3/h from a tank A, where the absolute pressure is 12,350 Pa, to a tank B, where the absolute pressure is 101,325 Pa, through a sanitary with 3.8 cm diameter and 4.6x10^-5 m surface roughness. The pump is 1 m below the liquid level in tank A and the discharge in tank B is 3.3 m above the pump. If the length of the pipe in the suction line is 2 m, the dischargeline 10 m, and there are one 90 degree anlge flanged elbow in the suction line, two 90 degree angle thread elbowsin the discharge line, and one globe valve in the discharge line. Calculate he pump power required for finishing this job, assuming the efficeincy of the pump is 65%.

Z table work with given standard deviation and average(mean)

1.   Given μ_X = 750, σ_X = 80

        a) Find the two X values that are 2.7 SD away from the mean

        b) Find X1 if p(720 < X < X1) = .428

        c) Find X0 if p(X0 < X < 910) = .347

        d) Find p((X < 700) or (X > 900)) (sum required)

        e) Find any X0 and X1 s.t. p(X0 < X < X1) = .338

        f) Find the value of X that is 3.8 SD below X = 725

2. a) Find Z1 s.t. p(Z < Z1) = .675  

      b) Find Z1 s.t. p(-2.48 < Z < Z1) = .3831

      c) Find Z1 s.t. p(Z > Z1) = .2015

      d) Find Z0 s.t. p(Z0 < Z < .77) = .334

• Please state the null and alternative hypotheses.
• Using an alpha level of .05, please test the null hypothesis (what is the appropriate test, what is the critical value?). Draw the rejection region.
• Calculate the test statistic
• State the conclusion you are entitled to draw as a result of this test.
• Calculate the effect size as appropriate for the hypothesis test used.

2. A current popular game relies on the rolling of twenty sided dice to determine success or failure. The current iteration occasionally uses rolling two dice, but only selecting the best roll to determine the outcome. An older edition merely modified the roll by 2 during these occasions. A sample of rolls under both conventions has been collected. The mean of 10 rolls using the two dice technique was 13.9 (SD = 3.8). The mean of 10 rolls using the older technique was 12.5 (SD = 4.4). Does the revised technique make a difference?  

An article in Solid State Technology, "Orthogonal design for process optimization and its application to plasma etching" by G.Z.Yin and D.W.
Jillie (May, 1987) describes an experiment to determine the effect of the
C2F6 flow rate on the uniformity of the etch on a silicon wafer used in
integrated circuit manufacturing. All of the runs were made in random order. Data for two flow rates are as follows:

C2F6     Uniformity Observation
Flow 1      2      3      4     5      6

125   2.7   4.6 2.6   3.0   3.2   3.8

200   4.6   3.4   2.9   3.5   4.1   5.1

a) Does C2F6 flow rate affect average etch uniformity? use a=0.05

b) What is the P-value for the test in part (a)

c)Does the C2F6 affect the wafer-to-wafer variability in each uniformity? use a0.05

d) Draw box plots to assist in the interpretation of the data from this experiment