I need help to understand what these numbers mean (i.e mean, SD, t critical, p value especially and hypothesis testing)

Somehow a score has been attributed to people's attitude toward childbirth (perhaps a Likert scale). Maybe the scale was 1-10, with 10 being strongly agree/support, and 1 being strongly disagree/against.

The mean is the average attitude score; higher average means (I'm guessing) people are more supportive of it. The SD is a measure of variation in people; smaller SD means more uniformity in people's attitude.

p value is the probability of rejecting the null hypothesis when it is actually correct. The smaller the p-value, the less likely you are to make this kind of error.

It looks like your null hypothesis is: the average attitude score is a 5. Using common sense (and not worrying about statistics for a second): if a method has an average score of 4.5 then you might be able to reject the null hypothesis but you do know that surveying people is not perfect, so maybe with a better sample this average would actually become 5. But if the method has an average score of 1.2 then you would likely reject the null hypothesis, and you would feel more safe in rejecting a sample average of 1.2 than 4.5. The p-value is a statistical way of measuring this "safeness".

The question is:

1.) how would you interpret the results from this table? decide whether they are favoried in vitro fertilization. Are they supporting it or not?

It's hard for me to help you with this one because I'm not used to seeing a table presented just like this. Were you given those t and p values, or did you calculate them yourself?

My interpretation of this table would be: in vitro, adoption, and childless are all significantly different from 5, while artificial insemination is not. Since in vitro is the only one with a mean > 5, then we can assume that it is the most favored method.

(note: I think most people would do 3 pairwise tests: in vitro vs. another method, to verify that people significantly favor in vitro, but if this table is all you have then you gotta give some answer...)

b.) Explain by looking at the mean and Sdevn for each 4 variables which survey opinion was captured more precisely.

It seems to me what this question is gettting at: the childless option has a mean attitude that is most different from 5 (the null average), and it has the smallest SD. So this was the opinion that was captured more precisely.