WHAT HYPOTHESIS TEST TO USE WITH NON-NUMERIC DATA?

Question

I have a question and I'm being asked to specify which test to use and then conduct it. However, the data given is non-numeric. the question statement is "males and females differ in whether or not they regularly eat breakfast" and the data given is like, ffffmmmfmmfm YYYNNYYNN. I was thinking paired t-test but I don't know what to work on! please help.

Answer 1

                              YES                             NO           TOTAL

     Males                  2                                  2               4

 

    Females                3                                  2               5

-------------------------------------------------------------------------------

    Totals                   5                                4                9

 

Please note that the data is INCOMPLETE!!!

There are 12 subjects questioned (6 females and 6 males)

but only 9 responses ( 5 yes and 4 No)

 

So the results are going to be invalid.

But for the sake of answering the question....

 

T-test for comparing two population proportions.

50% of the males in the sample eat breakfast,

while 60% of the females eat breakfast.

 

p = (p1 * n1 + p2 * n2) / (n1 + n2)

   = (50% * 4 + 60% * 5)/(4+5) 

   =  (2 + 3)/9

   = 5/9

 

 

Standard Error:

 SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

       = sqrt{  5/9 * (1 - 5/9) * [ (1/4) + (1/5)] }

 

       = sqrt{ 5/9 * 4/9 * [ 9/20 ] }

 

       = sqrt{  20/81 * 9/20 } 

 

       = sqrt {  1/9 }

 

       = 1/3

 

 

Test statistic:

  z = (p1 - p2) / SE

  

     = (50% - 60%)/ (1/3)

 

     = -10%/ (1/3)

 

     = -10% * 3

 

     = -30%

 

     = -0.3

 

No, there is sufficient evidence that the populations proportions

are the same.