代做Introduction to Quantitative Methods MIDTERM EXAM代写C/C++编程

MIDTERM EXAM

35 Points

Q1 (10 points)

The May  1,  2009 issue of The Montclarion reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):

590   815   575   608   350    1285   408   540   555   679

a. Calculate and interpret the sample mean and median.

b. Suppose the 6th observation had been 985 rather than 1285. How would the mean and median change?

c. Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations.

d. Calculate a 15% trimmed mean.

Q2 (10 points)

1.           Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.

a.    List all outcomes in the event A that all three vehicles go in the same direction.

b.    List all outcomes in the event B that all three vehicles take different directions.

c.    List all outcomes in the event C that exactly two of the three vehicles turn right.

d.    List all outcomes in the even D that exactly tow vehicles go in the same direction.

e.    List outcomes in D', C ∪ D, and C ∩ D.

Q3 (15 points)

Two different companies have applied to provide cable television service in a region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H0: p = .5 versus Ha : p ≠ .5 based on a random sample of 25 individuals. Let X denote the number in the sample who favor the first company and x represent the observed value of X

a.   Which of the following rejection regions is most appropriate and why?

R1 = {x: x ≤ 7 or x ≥ 18};

R2 = {x : x ≤ 8}; R3 = {x : x ≥ 17}

b.    In the context of this problem situation, describe what type I and type II errors are.

c.   What  is the probability  distribution of the test statistic X when H0  is true? Use it to compute the probability of a type I error.

d.    Compute the probability of a type II error for the selected region when p =  .3,  again when p = .4, and also for both p = .6 and p = .7.

e.    Using  the  selected  region, what would you  conclude if 6  of the 25 queried  favored company 1?