Question

1. A psychology professor at a university is interested in determining the proportion of undergraduate students at her university who self-identify as early-risers, night-owls, or neither. She decides to perform an observational study to investigate this question, so she randomly selects 500 undergraduate students from a university with 11088 undergraduate students enrolled to whom she poses her question. 274 respond that they would call themselves night-owls, 124 replied that 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 college students who identify as night-owls is larger than 0.33?

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

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

c. Yes, it is appropriate.

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

2. She now finds a 95% 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 where H0:p=0.33H0:p=0.33 and HA:p≠0.33HA:p≠0.33 be at an α=0.05α=0.05 significance level?

Clearly state the conclusion to the hypothesis test (reject/fail to reject/accept H0H0/HAHA), how you know this is the conclusion, and write a sentence interpreting your conclusion in the context of the problem.

Answer 1

c. Yes, it is appropriate since the conditions are met.

The sample size(500) is less than 5% of population size(11088)

the 10% conditions are met. (500*0.33>10)

(500*(1-0.33))>10

Random Sampling is done. Randomization condition is met too.

Reject H0 is the conclusion.

The confidence interval does not contain the value 0.33. Hence, we clearly see that we are 95% confident that the population proportion of self identifier night owls is within 0.504 and 0.592,which can never contain the value 0.33

Hence definitely reject null hypothesis which says p=0.33