UCSB PSTAT 109 Statistics for Economics Quiz7 Winter 2014

PSTAT 109: Quiz 7

Winter 2014

Instructions: Please show all formulas and calculations in an organized fashion for full credit.

Problem 1. For the following data,

21, 18, 17, 23, 22, 19, 21, 17, 25,

compute the following measures:

a. mean,

b. sample variance,

c. the 30th percedntile,

d. the median,

e. the 83rd percentile,

In general, what is the advantage of reporting the median value as opposed to the mean value?

Problem 2. Suppose X1 and S 2 1 are the sample mean and sample variance from a population with

mean 1 and variance  2 1 , and X 2 and S 2 2 are the sample mean and sample variance from a second independent population with mean 2 and 2

 The sample sizes are n1 and n2, respectively. Show that..

b. Now suppose we have the same setup as in (a) but 2 1 =  2 2 =  2 . Show that the pooled sample variance

is an unbiased estimator of 2 . (Hint: Sample variance S 2 is an unbiased estimator of population variance  2 .)

Problem 3. Candidate A is running for student body president at some university. The proportion of students who favor this candidate at the moment is 0.8.

a. Suppose a simple random sample of 100 students is taken. What are the expected value, standard deviation, and shape of the sampling distribution of p?

b. If a simple random sample of 100 students is taken, what is the probability that the number of students in the sample who DO NOT favor Candidate A will be between 26 and 30?