Castaneda v. Partida is an important court case in which statistical methods were used as part of a legal argument. When reviewing this case, the Supreme Court used the phrase "two or three standard deviations" as a criterion for statistical significance. This Supreme Court review has served as the basis for many subsequent applications of statistical methods in legal settings. (The two or three standard deviations referred to by the Court are values of the z statistic and correspond to P-values of approximately 0.05 and 0.0026.) In Castaneda the plaintiffs alleged that the method for selecting juries in a county in Texas was biased against Mexican Americans. For the period of time at issue, there were 180,025 persons eligible for jury duty, of whom 143,075 were Mexican Americans. Of the 860 people selected for jury duty, 346 were Mexican Americans.

(a) What proportion of eligible voters were Mexican Americans? Let this value be po. (Round your answer to four decimal places.)

(b) Let p be the probability that a randomly selected juror is a Mexican American. The null hypothesis to be tested is Ho: p = po. Find the value of p̂ for this problem, compute the z statistic, and find the P-value. What do you conclude? (A finding of statistical significance in this circumstance does not constitute a proof of discrimination. It can be used, however, to establish a prima facie case. The burden of proof then shifts to the defense.) (Use α = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)

z

P-value

Conclusion

Reject the null hypothesis, there is significant evidence that Mexican Americans are underrepresented on juries.

Reject the null hypothesis, there is not significant evidence that Mexican Americans are underrepresented on juries.

Fail to reject the null hypothesis, there is not significant evidence that Mexican Americans are underrepresented on juries.

Fail to reject the null hypothesis, there is significant evidence that Mexican Americans are underrepresented on juries.

(c) We can reformulate this exercise as a two-sample problem. Here we wish to compare the proportion of Mexican Americans among those selected as jurors with the proportion of Mexican Americans among those not selected as jurors. Let p1 be the probability that a randomly selected juror is a Mexican American, and let p2 be the probability that a randomly selected nonjuror is a Mexican American. Find the z statistic and its P-value. (Use α = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)

z

P-value

Conclusion

Reject the null hypothesis, there is significant evidence of a difference in proportions.

Reject the null hypothesis, there is not significant evidence of a difference in proportions.

Fail to reject the null hypothesis, there is not significant evidence of a difference in proportions.

Fail to reject the null hypothesis, there is significant evidence of a difference in proportions.

How do your answers compare with your results in (b)?

very different

very similar

none of the above

1) A cylinder of Mass M and radius R, and initial speed V, starts
rolling up an incline of angle theta relative to horizontal. Assuming
no slipping, how high up does the cylinder get?

2) teeter/totter
a) Peewee has mass m and his big buddy Delilah has mass 2m. If Peewee
sits at one end of a uniform teeter totter of length L and mass M, how
far from the central pivot should Delilah sit (ie on the other end) to
be balanced?

b) Delilah instead chooses to sit at the far end from Peewee. What
vertical acceleration does Peewee experience when they start from a
level teeter/totter from 0 angular velocity at horizontal? Provide an
answer that is a function of the angular displacement (theta) from the
horizontal. What normal force does Peewee experience as a function of
theta?

3) A baseball-crazy astronaut in space catches a fastball. What happens?
Let's treat the astronaut as a rod of length L and mass M and assume
the ball of mass m attaches a distance L/5 from one
end. Compute/describe the resultant motion. Note the moment of inertia
for a solid rod is ML^2/12 for rotation around its center of mass. Hint,
you will have to use the parallel axis theorem for moment of inertia.

The speed of a water wave is described by v= (gd)^(1/2)  where d is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth.

Suppose waves approach the coast from a storm far away to the north–northeast. Demonstrate that the waves move nearly perpendicular to the shoreline when they reach the beach.

Suppose waves approach the coast, carrying energy with uniform density along originally straight wave fronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays.

A 150-V battery is connected across two parallel metal plates of area 28.5 cm² and a separation of 8.20 mm. A beam of alpha particles (charge +2e, mass 6.64E-27 kg) is accelerated from rest through a potential difference of 1.75 kV and enters the region between the plates perpendicular to the electric field.

What magnitude and direction of magnetic field are needed so that the alpha particles emerge undeflected from between the plates?

Using the data in the following table, answer parts (i) – (v).

1. Estimate the average return for each stock.   
2. Calculate the standard deviation of returns for Stocks X and Y.   
3. For a portfolio that is 75% weighted in Stock X, and 25% weighted in Stock Y, calculate the expected return of the portfolio.   
4. Calculate the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (iii).  
5. Suppose the correlation between Stocks X and Y has reduced to 0.35, does it increase or reduce the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (iii). Explain your answer.

Transverse waves on a string have wave speed v = 8.00 m/s, amplitude A = 0.0700 m, and wavelength λ = 0.320 m. The waves travel in the -x direction, and at t = 0 the x =0 end of the string has its maximum upward displacement.

1) Find the frequency of these waves.

2) Find the period of these waves.

3) Find the wave number of these waves.

4) Write a wave function describing the wave. Express your answer in terms of x and t. Use π as constant.

5) Find the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s. Express your answer in meters.

6) How much time must elapse from the instant in part E until the particle at x = 0.360 m next has maximum upward displacement? Express your answer in seconds.

In Drosophila, the X-linked recessive mutation vermillion (v) causes bright red eyes, in contrast to the brick-red eyes caused by the wild-type allele. A separate autosomal recessive mutation, brown (bw), causes flies to have brown eyes. Flies with both mutations have no eye pigmentation and are white-eyed. Determine the F1 and F2 phenotypic ratios for each sex from the following crosses:

(a) vermillion females X brown males

(b) wild-type females X white-eyed males

Examine and summarize the case of Tinker v. Des Moines Independent Community School District. In your paper explain the background of the case, the progression of the case to the Supreme Court, the Supreme Court’s decision and justification for the ruling as it relates to State control over schools. Compare and contrast the decisions of the various courts and how the case progressed. What might be a similar situation today? Why is this considered such an important case? Your paper should be 3-5 pages in length. Use the items listed in these instructions as subheadings.

Read Case Summary 3.7 Mosher v. Benson on page 85. This case is about a 17 year old who purchased a car from an adult. The 17 year old (Mosher) asked to have the transaction reversed on the basis that he was a minor at the time of the contract.

Answer the following questions:

1. This case is from the province of Nova Scotia. How would this case likely be resolved in a British Columbia court? Answer this question by describing the relevant law in British Columbia.

2. Do you believe that a car should be considered a necessity? Why or why not? Consider what the definition of a necessity is in your answer.