I'm stuck on this problem & I need help:

1) Use R as a calculator to do the "by-hand" calculations (meaning, show the steps as if you were solving by hand) to test a claim that the population proportion of green-eyed students having blue hair is different than the proportion of hazel-eyed students having green hair, using a 5% significance level. Show your work in the R chunk. Assume large sample conditions are met. [be sure to follow all steps for hypothesis testing for this part] (1 hypothesis, 1 by-hand calculation, 1 reporting required numbers, 1 decision, 1 interpretation in context)

2) Repeat the test in part 1) using prop.test in R. No need to state the hypotheses and other information, as you should get comparable results and the same conclusion. Show that the square root of the chi-square test statistic from prop.test is equal to the z-score you got in part (1), within rounding error.

3) In the context of this problem, what does it mean if a Type 2 error was committed? Are there are any significant consequences if a Type 2 error was made?

Any help is appreciated; thanks!