An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treated sheep 18, 43, 28, 50, 16, 32, 13, 35, 38, 33, 6, 7

untreated sheep 40, 54, 26, 63, 21, 37, 39, 23, 48, 58, 23, 39

(a) Construct a 98% confidence interval for the difference of the worm count in a lamb.

(b) Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.

(c) What are your assumptions that you assumed in part (b)

An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.
∑X = 50
∑X² = 200
∑Y = 75
∑Y² = 1600
∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

An experiment was conducted to determine if there was a mean difference in weight for women based on type of aerobics exercise program participated (low impact vs. high impact). Body mass index (BMI) was used as a blocking variable to represent below, at, or above recommended BMI. The data are shown as follows. Conduct a two-factor randomized block ANOVA (alpha = .05) and Bonferroni MCPs using SPSS to determine the results of this study.

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 47.5 km due north. A detector is placed 116 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector.

(a) When properly aligned, what angle should the normal to the surface of the mirror make with due south?

(b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.005

In an experiment on the photoelectric effect, a beam of monochromatic light is aimed at a nickel-plated cathode. A scientist uses mathematical formulas to calculate the maximum speed of the electrons that the cathode releases. Which constant most limits the precision of the calculation?

Which example illustrates a behavior called “photoconductivity”?

A metallic film conducts electricity when an electric potential is applied across it.

A cathode emits electrons when it is struck by white light, which is a mixture of light of many frequencies.

A film with metallic properties becomes a better electrical conductor when light is shined upon it.

A cathode emits electrons when monochromatic light of a certain frequency strikes it.

Let ? be the sample space of an experiment and let ℱ be a collection of subsets of ?.

a) What properties must ℱ have if we are to construct a probability measure on (?,ℱ)?

b) Assume ℱ has the properties in part (a). Let ? be a function that maps the elements of ℱ onto ℝ such that

i) ?(?) ≥ 0 , ∀ ? ∈ ℱ ii) ?(?) = 1 and iii) If ?1 , ?2 … are disjoint subsets in ℱ then ?(⋃ ??) = ∞ ?=1 ∑ ?(??) ∞ ?=1 . Show that 0 ≤ ?(?) ≤ 1, ∀? ∈ ℱ.

c) Is every subset of ? necessarily an event? Explain briefly. Rigorous definitions are not necessary.

d) Assume ℱ has the properties in part (a). Let ? and ? be any two subsets of ? that are elements of ℱ.

i) Show that (? ∩ ?) ∈ ℱ.

ii) Show that (? ∖ ?) ∈ ℱ, where (? ∖ ?) is the set of outcomes that are in ? but not in ?.

iii) Show that (? △ ?) ∈ ℱ, where (? △ ?) is the set of outcomes that are either in ? or in ? but not in both.

iv) Let ?1 , ?2 , ?3 … be elements of ℱ. Show that ⋂ ?? ∞ ?=1 ∈ ℱ

As an engineer you are responsible to in charge to conduct an experiment for this traffic flow analysis: At 2:00 P.M. a traffic accident closes a road to all traffic. At 2:15 P.M. the road is partially opened with a capacity (car departs) of 1,500 veh/h. Finally, the wreckage is removed, and the road is restored to full capacity (car departs) (3,500 veh/h) at 2:35. From 2:00 to 2:35, car arrives at a constant flow of 2,500 veh/h and then drops to 2,000 veh/h thereafter. Assume D/D/1 queuing to determine

1. Total delay: __________ veh-min

1. Longest vehicle delay under LIFO _________ min

1. Time of queue dissipation: ___________ min

Queue length at 60 min: ___________veh

1. Longest (max) wait of any vehicle (assuming FIFO): ____________min

1. Longest (max) queue length: ____________ veh

1. how a graphical representation of the solution and clearly label the parameters and axis with the appropriate units accordingly.

The results of a tensile experiment on a metal is given in the table below. The tensile sample had circular cross section with the diameter of 10 mm and initial gauge length of 60 mm. Use this table and calculate:

(a) The Young modulus of this metal (in GPa)

(b) The modulus of resilience (MJ/m3 )

(c) The measured diameter of the sample is 9.5mm when the applied force is 37306N. What is the Poisson’s ratio?

(d) What is the engineering stress and strain, as well as the true stress and strain at the applied force of 37306N?

An experiment was performed to determine the efficiency of a transformer. A coil is placed into another coil, and a steel bar is placed on the inside of both coils.

f (efficiency) = V1*N2 / V2*N1

Suppose we ignore the possibility of someone having miscounted the number of turns. Why might "1 turn" (or, perhaps, "1/2 turn") still make sense as an uncertainty on the number of turns?

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 52.0 km due north. A detector is placed 107 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector.

(a) When properly aligned, what angle should the normal to the surface of the mirror make with due south?

(b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.005