MR method must be used.

I need help for b-d! I'm not sure for B if I should compare the sample size with either 10 or 30. I think it's 10 since we're talking about proportion, but I'm not sure!

A case-control study compared short to non-short English secondary school students. Of n = 92 short students, 42 said they had been bullied in school. Of n = 117 non-short students, 30 aid they had been bullied in school. The researchers wanted to know whether short students are bullied more often using a 5% significance level. Let S denote short and NS denote non-short. a) Define the null and alternative hypothesis for testing the researchers claim in both words and symbols. b) Is the large enough condition satisfied for conducting this test? Explain. c) What sampling distribution does this test rely on? d) The software (R) output for running this test is shown below. What do you conclude for this test? Include your decision and an interpretation in the context of the problem. Be specific. data: c(42, 30) out of c (92, 117) z = 3. 022, p-value = 0. 002017 alternative hypothesis: greater sample estimates: prop 1 prop 2 0 . 4565217 0. 2564103