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.

What would be the best statistical test to use to test whether the student's hypothesis is supported based on this data?

Carry out the test. What is the p-value given by the test? Is her hypothesis supported?

What are the best estimate and the 95% confidence interval for the proportion of plants that will survive a similar summer in future if they are planted with water-holding beads?