Statistics

MATH220--Assignment 1

Question 1. (Minitab) The weights (in grams) and humerus lengths (in inches) of 35 male house sparrows that survived and 24 that perished from a severe winter storm were recorded. The data file is provided separately.

a)      Describe the individuals and the variables in this study. Specify the quantitative and the categorical variables?

b)      Construct a stem-and-leaf display (or stemplot) of the distribution of the humerus lengths of the 59 male house sparrows.

c)      Describe the shape, center, and spread of the distribution of humerus lengths.  Identify any suspected outliers.

d)     Make back-to-back stemplots of the humerus lengths for the male house sparrows that survived and those that perished. Write a brief comparison of the two distributions.

Question 2.  (Minitab)  How do cigarette excise taxes per 20-pack (in dollars) vary from state to state? The data set of the 2011 cigarette taxes for the 50 states, the District of Columbia, Guam, Puerto Rico, and Northern Marianas Islands is provided separately.

a)      Make a histogram of the data.

b)      Describe the distribution of the cigarette excise tax in the 54 states o regions. Use percentages to enrich your description.  Identify the outlying regions, if any. Say something about cigarette taxes in your native and/or adopted state or region.

c)      Look at the map of the 2011 state cigarette excise tax  in

http://www.ncsl.org/issues-research/health/2011-state-cigarette-excise-taxes.aspx

Are there regions of the country where cigarette taxes are higher or lower?

Question 3.  (Excel) Solve the following problem:

Question 4. (Minitab) The U.S. annual average unemployment rate is an important economic indicator.  Data (in percent) on the seasonally adjusted unemployment rate between 1948 and 2012 are provided separately (source: U.S. Bureau of Labor Statistics). Make a timeplot of the annual average unemployment rate and describe the pattern of the series over time. By digging a little bit in the recent history of the United States, try to explain the unusually highs and lows of the unemployment rate.

Minitab Instructions for Assignment 1

The data sets for Assignment #1 can be found in the Assignments section in ACE. You can access Minitab directly from ACE by double clicking on the data set for the problem you would like to work on (for example Pb 1.MTW for problem 1).

You will need to open an MS Word file in which you will be storing your MINITAB output, graphs, and answers to questions. Save your word file!

Question 1.

To construct the stem-and-leaf display:

-          Choose GRAPH  →  Stem-and-leaf.

-          Select the Humerus Length variable for the Variables box

-          Deselect the ‘Trim outliers’ box and press Enter.

-          Copy the output from the session window and paste it to your MSWord file.

d)  MINITAB does not do back-to-back stemplots. The steps below will give you the weight distributions for the two groups.  We will use the output and a 2 x 2 table in MSWord to align the stemplots side-by-side:

-          Choose GRAPH  →  Stem-and-leaf.

-          Select the Humerus Length variable for the Variables box.

-          Check the By Variable box and enter the Status-coded variable. Note that 0 = Perished and 1 = Survived.

-          Press Enter (the output will consist of two individual stemplots).

-          Copy and paste the individual stemplots in your Word file as follows:

o   Create a 2x2 table in your MS Word file.

o   In column 1, enter the legend and the stemplot for the “Perished” group  in row 1 and row 2, respectively.

o   In column 2, enter the legend and the stemplot for the “Survived” group in row 1 and row 2, respectively.

Question 2.

a)To obtain the default histogram for the pH:

-          Choose GRAPH  →  Histogram.

-          Select the Simple histogram and click OK

-          Select the Excise Tax variable for the Graph variables box

-          Click on the Labels button and select Data Labels

o   Choose ‘Use y-value labels’—the labels will be the absolute frequencies—and press Enter

-          Click on the Labels button (Title/Footnotes tab) and give a title to the graph

-          Press Enter twice

Question 3.

a) Open the data file (you will be using Excel)

-           Highlight City and Population columns

-          From the Insert Menu select the ‘Column’ bar chart icon (select the 2-D chart)

b) Repeat for City and Open Space.

c) You are on your own for the rest.

Question 4. To obtain the timeplot for the annual average unemployment rate:

-          Choose GRAPH → Time Series Plot

-          Select the Simple plot and click OK (double clicking works too)

-          Select the annual average unemployment rate for the Series box and press Tab

-          Click on the Time/Scale button

o   Enter 1948 in the Index BOX and press Tab

o   Enter 1 in the Increment box and press Enter

-          Click on the Labels button (Tiltle/Footnotes tab) and give a title to the graph

-          Press Enter twice