Mathematical Statistics—Homework Assignment #1

Due Friday, January 15 (beginning of class)

Important Reminders

Please respect me, your classmates, and yourself by taking the Honor Code very seriously. Your grade will depend on both the content and exposition of your answers. That is, be sure your logic is clear, you defend all your steps (unless they are, for example, obvious algebra steps), your solutions read smoothly (even if using symbols—they should still read like an English sentences), and that one of your peers could read and understand your solutions without asking any additional questions. When doing data analysis, be sure to use complete, specific, contextual sentences in your interpretations.

Minitab

Use Minitab for problems 69 and 70 in Chapter 1. (Recall Minitab is on the LU network, so you can access it from any computer lab.) The data files are in the math_445 share folder (on the U: network drive). Although not required, it might be most convenient for you to copy graphs and numerical summaries from Minitab to Word (resize graphs so they aren’t so big), and then type your interpretations.

Okay-to-work-together Problems (5 total problems)

Chapter 1: 70, 76

Chapter 6: 35 [Recall . Also, . ], 75

Additional Problem 1:

In the spring of 1991, the engineering department (in the envelope division) of Westvaco Corporation had five rounds of layoffs. At the time of the second round of layoffs, there were 10 hourly-wage employees who worked in the engineering department. The ages (in years) of these employees are listed below.

25 33 35 38 48 55 55 55 56 64

During the second round of layoffs, three of the hourly-wage workers were laid off. The ages of these three employees were 55,55, and 64. Robert Martin, one of the laid-off employees, filed a lawsuit against Westvaco claiming the company practiced age discrimination in deciding who would be laid off during the second round.

a. Can we make a claim of age discrimination based solely on these data (i.e., the ages), or is there other information you would like to have? If so, what information would you like to know and why?

b. If there was no age discrimination, then we could possibly assume the ages of the three laid-off employees are simply a random sample from the population of ages (since age has nothing to do with the layoff process). Create the population of 10 ages by writing each age on a piece of paper. Then mix up the cards (ages face down)—this process is important to ensure the randomness. Now draw three cards, record the ages as your first sample, and calculate the average age for your sample. Repeat this process 20 times. Now create a dotplot (you can do this by hand) of your 20 average ages. This is a partial sampling distribution of the average age of laid-off employees, assuming no age discrimination. Where does the average age for the three Westvaco employees fall on your sampling-distribution graph? Use this information to make a case for or against age discrimination.

Work-alone Problems (6 total problems)

Chapter 1: 69 (no units given)

Additional Problem 2:

A teacher wants to estimate the average number of children per family (for families that have children). She has a large class of students, who represent a diverse population. She asks each student, “How many children are there in your family, including yourself?” Then she averages these values to determine an estimate of the average number of children per family in the population. Is this sampling method appropriate or biased? Carefully explain your answer (and if you think it’s biased, say whether the teacher’s estimate will be high or low).

(Continued on back-side of page)

Chapter 6: 5, 17, 71

Additional Problem 3:

Consider four different distributions: 1) The distribution of the number of Facebook friends for a population of 1000 college students, 2) the distribution of Facebook-friend values for one sample of size 200 (taken from the population described in 1), 3) the distribution of number-of-Facebook-friend averages for 1000 different samples (all of size n=10) from the population mentioned in 1, and 4) the distribution of number-of-Facebook-friend averages for 1000 different samples (all of size n=50) from the population mentioned in 1.

Four frequency histograms are shown below. Match each histogram with exactly one of the distributions listed above. Thoughtfully defend your answer for every match (not just “it was the one leftover”).