Hypothesis Test Statistics Problem

[FullestHarp43]

My current work is attached.
I completed part A of the question, but I'm not sure whether its completely correct. I'm also unsure what the third assumption is in part A, or how to do part B. Can you help?

The question:

1) It is estimated that 17.4% of all US households own a Roth IRA. The American Association of University Professors (AAUP) believes this figure is different among their members and commissions a study.


a) If 150 out of a random sample of 750 AAUP members own Roth IRA’s, is this sufficient evidence to support the AAUP belief at the α=0.05 level? (You must run a hypothesis test)

b) Based on your results from (a), if an error was made, would it be type I or type II error? Explain the error you chose in the context of the question.

 

[mikegonz00]

I can help with part b. There are two types of error when it comes to hypothesis testing: Type I error and Type II error. Type I error is the event that (say, after you've performed the hypothesis test and made a conclusion) you reject the null hypothesis, given that the null hypothesis is actually true. Type II error is the event that you don't reject the null hypothesis, given that the null hypothesis is actually false.

You should think about whether or not you've rejected the null hypothesis in your solution and think about what that implies about the only type of error that you could've performed. Hope that makes sense to you.