1. A psychology professor at a university is interested in determining the proportion of undergraduatestudents at her university who self-identify as early-risers, night-owls, or neither. She decides to performan observational study to investigate this question, so she randomly selects 500 undergraduate students from a university with 29016 undergraduate students enrolledto whom she poses her question. 274 respond that they would call themselves night-owls, 124 repliedthat they are early-risers, and 102 respond that they are neither.

Is it appropriate to conduct a hypothesis test for proportions, testing whether the proportion of collegestudents who identify as night-owls is larger than 0.33?

Select one:

a.No, because the professor conducted an observational study.

b.No, because the assumptions necessary for inference are not met.

c.Yes, it is appropriate.

d.No, because the professor's question had 3 possible answers.

If there were any issues with the hypothesis test, the professor corrected them and repeated the study.

She now finds a95% confidence interval for the proportion of college students who self-identify as night-owls to be(0.504,0.592). What would the conclusion of the hypothesis test whereH0:p=0.33 andHA:p0.33be at an=0.05 significance level?

Clearly state the conclusion to the hypothesis test (reject/fail to reject/acceptH0/HA), how you know this is the conclusion,and sentence interpreting your conclusionin the context of the problem.