Hypothehis test (Z- two simple proportion). I'm try to understand from where came this numbers.

Question

I'm trying to find out from where came some proportions in a hypothesis test problem from my class notes. Here is the problem and tables:

Statement "X"

Pm= the proportion of men who agree with the statement.

Pf= the proportion of women who agree with the statement.

Ho: Pm=Pf

Ha: Pm>pf

*The sample sizes in both groups are large and we can thus use a two- population z-test for proportions.

Notes from class said: (I'm lost here)

pM = 0:242; 
pF = 0:216;  
p = 0:228;  
q = 0:772;


nM = 810; nF = 1060 (This two values I have it easy from the table)

The Z statistic from notes:

Question: I'm sorry if this is a silly question, but I have no idea from where were obtained the values to compute the z statistics. If someone can't help me with this it will be apreciaste. Thanks!

Answer 1

Here I compute the values you asked for,

Pm = 198 men agree with X over 810 that(total of men) is equal to 0.244 but not 0.242 

Pf= 229 women agree with X over 1060 (total of women) is equal to 0.216 

P=(198+229)men and women who agree with X over the total which is 1870 is equal to 0.228 and

q=1-p also match.

I believe is an error in your notes, for Pm.