Fitting Probability Models to Frequency Data

Assignment 8—Questions from Chapter 8  “Fitting Probability Models to Frequency Data”

(52 pt)

• Please type your final answers to the problems on the main pages of your assignment. After the pages with typed answers, attach handwritten pages showing your calculations.  On the pages of calculations, clearly indicate the problem numbers and final answers.  For calculations using a X² test, include a table of observed values, your calculations for expected values, and a table of expected values, on the handwritten pages.   Don’t use computers for the analyses.

• Directions for reporting results of statistical tests—on the typed pages, report:

–state the null and alternative hypotheses

–n (sample size)

–degrees of freedom

–alpha (Threshold level of significance.  Decide on the value before doing the statistical test.  The default is to test at alpha = 0.05, meaning at the 5% significance level.)

–the name and value of the test statistic (Example:  X² value = 0.55)

–p-value (from a table of critical values in the back of the textbook)

–Describe your conclusion in a sentence.  (Example 1:  “Births are not evenly distributed over the days of the week.”  Example 2:  “The proportion of wild-type flies was significantly greater than expected by the 3:1 ratio.”  Example 3:  “The proportions of people who are interested in each of the five areas of psychology are significantly different.”

• For practice problems, please write an answer in your own words before checking your answer against the solutions in the back of the book. Then, compare the solution to your answer.  If your answer wasn’t correct, don’t change it–write about how the solution in the book differed from your answer and why it’s correct.  In other words, show evidence that you are thinking independently and learning.  In this way, you can get full credit even if you originally didn’t have the correct answer.

• Please type and staple and put your name and the number or title of the assignment on the first page. Print and hand in during class.  If you miss class or need to turn in a late assignment, upload your assignment to Dropbox on D2L.

Practice problems:

3c  (8 pt)  Follow the directions for statistical tests.  (Don’t answer the second question of 3c because you didn’t do 3a.)  Attach pages with hand-written calculations at the end of the assignment.

3d  (2 pt)

6  (8 pt)  Use the data from problem 5 in chapter 7, but don’t answer the questions for problem 4.  Only answer this question:  Test whether the cancer rates in this group were different from the expected rate of 14%.  Do by hand and follow the directions for statistical tests.  Attach pages with hand-written calculations at the end of your assignment.

Assignment problems:

13a  (4 pt)

13b  (1 pt)

13c  (1 pt)

13d   (8 pt)  Follow the directions for statistical tests.  Do by hand and attach pages with hand-written calculations.

15a  (4 pt)

15b  skip

15c  (4 pt)

15d  (8 pt)   Don’t do by hand.  Instead, test the hypotheses using the chi-square goodness of fit test online at Vassarstats.net.  See the directions below.

How use Vassarstats.net for chi-square goodness of fit test

Follow this pathway:  Frequency Data>>scroll down the page to “Chi-square ‘Goodness of Fit’ Test” and click on it>>Enter the numbers observed (not percentages) in “Observed frequency”. If the expected numbers aren’t equal across categories, you’ll have to calculate them first yourself before entering them.  Use the percentages to get the expected numbers.  Enter the expected numbers (not percentages) in “expected frequency”.  Report each of the elements of a statistical test that are listed in the directions at the top of this page.  If df = 1, then report the corrected value of chi-square.

21. (2 pt) Hint: consider the assumptions of the chi-squared goodness of fit test.  The assumptions are given on p. 212.  The assumptions have to be true for you to use the test.  You may be able to combine categories to make the assumptions true.

Not from the book:

1  (2 pt)  What kind of variable does the chi-squared goodness of fit test require? (See top of p. 204 or lecture notes.)

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At the end of your paper, please write “Number of hours I spent on this homework:” and add an estimate.  Don’t include time that you spent reading the chapter.  This number won’t affect your grade.