# POLS 3316. Quantitative Methods

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POLS 3316. Quantitative Methods

Dr. Scott Basinger

Homework Assignment #3

Distributed Tuesday, September 26

Due Tuesday, October 3

Suppose you are a forest ranger, and as part of your job, you are required to check the health of various trees within

your park. Below are the ‘diameter at breast height’ (dbh) of five Douglas Fir trees in part of a forest. Treat this data as

the population of Douglas Fir trees. On all questions, round to two decimal points (see my “for example” below). When

calculating means and standard deviations use N in the denominator.

Tree: # 1 # 2 # 3 # 4 # 5

Diameter (dbh): 12.4 cm. 14.5 cm. 15.2 cm. 17.8 cm. 19.1 cm.

1. What is the average diameter of a Douglas Fir tree in the forest? μ = _____

What is the standard deviation of the Douglas Fir trees’ diameters? σ = _____

The next problem requires you to create a sampling distribution for this population, for a given sample size, and then

characterize the sampling distribution, just as we did with the turtles example in lecture 8.

1. Suppose you have a deadline to meet, and Douglas Fir trees are difficult to find within the forest, so you only have

time to locate three of the five trees. Identify all the feasible samples of size n = 3 trees and calculate their sample

means.

Sample: Sample mean:

For example: { 1 , 2 , 3 } 14.03 cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

{ , , } cm.

1. What is the mean of the sampling distribution of sample means for n = 3?

What is the standard deviation of the sampling distribution of sample means for n = 3?

Note: the standard deviation of the sampling distribution is NOT the same thing as the s.d. of the population!!!

Rather, it is the standard deviation of the ten sample means that you should have calculated in question 2.

1. Suppose you are a fan of baseball, and especially of the Houston Astros. Suppose further that you are engaged in a

debate or discussion with a friend about baseball, and the topic comes up of how many runs per game the Astros score.

Excuse yourself from the imaginary conversation, and carry out the following analysis:

1. a) Find data on the Astros season. For example, go to a website like https://www.baseballreference.

com/teams/HOU/2017‐schedule‐scores.shtml

1. b) Choose a sample of exactly 9 games; the easiest way to do this is to pick a starting date, and then look at the

eight subsequent games. (Note that this is not a “simple random sample,” but it is plausibly random.)

1. c) Fill in the following table:

Date Opponent Runs scored by

Houston

Runs scored by

Opponent Win or Loss?

1. d) Calculate the mean number of runs scored by Houston in your sample. 􀝔̅ =
2. e) Calculate the standard deviation of runs scored by Houston in your sample. s =
3. f) Calculate the “five number summary” for runs scored by Houston in your sample <__,__,__,__,__>
4. g) Draw the box‐and‐whisker plot based on this sample on a separate sheet or in this space:

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