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