Test Type Help

#1
Can someone please help me?

I just spent an hour writing a really detailed explanation of my stats project and it ended up getting deleted when I tried to preview post.

Basically all my data is here

I'm doing this for an AP Stats project and I'm really confused about what kinda of test I should be doing.

I randomly selected 34 people to take my survey which is trying to find out whether a person's personality traits (how they feel their personality traits are) compare to their given zodiac personality traits. When I did further research I found that the zodiac symbols dates technically change so I want to test both the traditional zodiacs with the new zodiacs (dates are different). So in the spread sheet it gives their date of birth, and the personality types they choose (for both a strength and a weakness which were created based off each zodiac). Then I determine whether the personality they choose (the associated zodiac) is the same as their traditional zodiac or non-traditional zodiac (which differ by date as mentioned earlier). Thats where the yes and no columns are. The two columns to the very right are the zodiacs that did associate with there answers.

The problem I don't know what test to do. I've tried a one sample proportion z-test and ended up with the results below:

Ho: p = 0
p: (# of people who guessed their zodiac strength to be same as their traditional zodiac)

Ha: p > 0

n = 34; p = 3/34; alpha level = 0.05

Conditions: (! = Not)
Random: SRS
Normal: np > 10 and n(1-p) > 10 34(3/34) = 3 !> 10 34(31/34) = 31 > 10
So the normal condition did not pass on one end, but I will proceed anyways.
Independent: True...

So after this I found the test-statistic by going:
(0 - p)/sqrt((p * (1-p))/34) = about -1.81

From this I find the pValue: 0.0351

From this I can conclude that we have enough statistically significant evidence at the 0.05 alpha level to reject the null hypothesis. However I can't shake the feeling that I'm going about this all wrong + I believe that with such a small proportion that my null hypothesis should be about correct. Can someone please just point me in the right direction? Thanks!
 
#2
I am not sure on what exactly to suggest, but i will provide a few points to ponder

When you say Ho: p=0, you want your null hypothesis to be that no person have the same traditional zodiac signs as their traits.
Personally, i would like to test something like
Ho: p>=0.5
H1: p < 0.5

Additionally, this would make your conditions np>10 and n(1-p)>10 valid.

believe that with such a small proportion that my null hypothesis should be about correct.
If looks at pure pecentages also, it doesn't seem that way
3/34~8.8%
you are comparing this with 0%
 
#3
Thanks for the suggestion but I ended up going about it like this:

Since there were 12 zodiacs, this would mean if a person randomly selected one they would have 1/12 chance of getting the correct one thus leading me to setting my

Ho: p = 1/12

and

Ha: p > 1/12

I also went about my testing wrong but thanks for the help anyways! :tup: