Which Significance test do I use?

#1
Hi, I've just started a new stats unit and it turns out my brain is a little dustier than I first thought. Would someone be able to give me a hint about which significance test to use for these questions?

Question 1 -
A student plants 76 seedlings of a rare species to see if they will survive the summer. With 36 of the seedlings she plants them with water-holding beads, while the rest are planted without. At the end of the summer, she finds that 27 of the seedlings she planted with water-holding beads have survived, while 21 of the ones planted without the beads have survived. Her hypothesis is that the beads should increase the survival of the seedlings.

Question 2 -
Some researchers have developed a theory regarding the genetics determining resistance of a certain weed to a particular herbicide. According to this theory, one quarter of the plants raised in an experiment should be killed by the herbicide and three quarters should survive. When 50 plants are raised and sprayed with the herbicide, the researchers find that 32 of them survive and 18 die.
To significance test to test his 'theory'.

I think in the second one you would use a binomial test, but I'm a bit unsure about how to do it. Question 2 goes on to ask about confidence intervals, how do I find a confidence interval if I'm conducting a binomial test?

Thanks for you help :)
 
#2
I think for question one I would think of using a non-parametric test. I'd be thinking how I could compare the observed frequency distributions to the expected frequency distributions.

And it looks like question two would require a similar method of testing.
 
#3
Hi, thanks for your help :)

I've had a look at the common parametric tests that are out there and I think I'm a little more confused :/

The only tests that really seem to use this type of data (ie. not using averages) is the chi-squared test or the fishers exact test. Both of these appear to use data with contingency tables - so would it still apply to my problems?

I thought about using a proportions test (though this is parametric, isn't it?) which seemed to fit but I was using examples from here: http://stattrek.com/hypothesis-test/proportion.aspx and they said something about the population needing to be 10 times the size of the sample... so it wouldn't be appropriate then?

Thanks...