Percentages, Expected Frequencies and Chi-Square
 
This assignment should be done first on paper.  Then open the PercentQuiz on WEBCT and enter your answers.  The WEBCT does not include the questions, it is just an answer key.  You can take the quiz as often as you like and the highest grade will count.  When the Quiz closes, however, there is no extension for late quizzes.

The answers must be typed precisely according to the rules for the software to mark them correct.  This means three significant digits, although leading zeroes should not be typed. There should be one digit after the decimal point, even if it is a zero.  This 6.7% or 53.7%  or 17.0% are correct for percent questions.   54% would not be correct, nor would 06.7%.  Expected frequency questions should NOT have a percent symbol (%) because they are not percents.  They should have three significant digits, e.g., one number to the right of the decimal point.  Thus, 54.2 would be correct but 45.2% would not because it has a percent sign.    45.7321  would be incorrect for being overly precise, having too many decimal points.  This may not be mathematically incorrect, but WEBCT doesn't know that, it looks for the precise form that I type in.  The questions will be numbered PCT1, PCT2, etc. and you just type in the answers.  You should get your result right away if you click all the boxes.  If you do not, go to the Quiz page, click on "completed" and then click on the "1" or "2" and the machine will grade it for you.

Consider the following answers to the question "I believe that marinated artichoke hearts should be the national vegetable."

35 men agreed
25 women agreed
85 men disagreed
125 women disagreed

Answer the following questions:

What percent of the men agreed?   PCT1 .           .
What percent of the women disagreed?  PCT2 .           .
What percent of those who agreed were men? PCT3 .           .
What percent of those who disagreed were women? PCT4 .            .
What percent of the respondents agreed? PCT5 .            .
What percent of the respondents were women? PCT6 .         .

Fill in the Table:

Gender and Belief that the Marinated Artichoke Hearts Should be the National Vegetable


Men Women Total
Agree . . .
Disagree . PCT7 .      . .
. 100%  
100%
 100%

Now, try figuring out some expected frequencies.  What would you expect to be the cell frequencies if there was no difference between Men and Women on the issue, given the marginal frequencies provided in this table?  (Note that these are different from the marginal frequencies calculated in the previous question.)

Men Women Total
Agree PCT8.   . . 25
Disagree . PCT9 .  .
 115
. 55 85 140

Now compute the Chi Square Statistic, using the WEB Chi Square Calculator. For this exercise, use the numbers from the original table:

35 men agreed
25 women agreed
85 men disagreed
125 women disagreed

Check the box for "Chi Square with Yates Correction" and "two tailed".  

   Enter the Chi Square Statistic, exactly as the WEB calculator gives it. PCT10 .      .

   How many degrees of freedom are there in this table?  PCT11 .       .

   Is this "statistically significant" by conventional criteria?  PCT12  Yes or No (multiple choice on WEBCT)