Hypothesis testing

Over a long period of time in Enrico's restaurant the ratio of non vegetarian meals to vegetarian meals is 2 to 1. In Manuel's restaurant in a random sample of 10 people oerdering meals, 1 ordered a vegetarian meal. Using a 5 percent level of significance test whether or not the proportion of people eating a vegetarian meal in manuels is different to that in Enrico's.

So i was doing this question and you have to use a two tailed test.

Firstly, Is it only really nessasary to test for p<1/3.

And secondly it turns out that it is not significant but if it was in the conclusion would you say that that p is not equal to 1/3 or would you say that p was less than 3 (if it turned out that the prob of X<or equal to 1 was less than 0.025.

Thanks for your help

Since you're asked to test whether the proportions are different (i.e. not equal), then I'd think a two-tailed test, with the two critical regions.

Confirm that you test statistic is, or is not, in each.

And conclusion, if value not in critical region: There is no evidence at the 5% level that the proportion of vegetarian meals at Manuel's restaurant is different to that at Enrico's.
(the wording of the conclusion ties back to the test you were asked to perform - in red in the quote above)

Thanks but if you were told to do a not equal to test and found it was actually lower would you say it was lower or different or does it not matter