1. My friend and I recently got into an argument about whether people's favorite seasons are aligned with their personalities.

To test this, I had 150 individuals take a personality inventory that gave a summary of their personality. I then matched each of these summaries with the season that I felt was best aligned with that person's personality. Afterwards, it was revealed what season was actually each person's favorite and we compared that with season I assigned them. The data revealed that 51 of the participants had been correctly matched to their favorite season.

What doe we conclude?

a) (4 pts) what is the research hypothesis and what is the null hypothesis?

b) (3 pts) What kind of problem (simulator) is this and what are we modeling?

c) (7 pts) How did you set up your simulator and why? (number of coins or matches, what does heads represent what was the probability of heads, why?)

d) (4 pts) What does one run of the simulator represent?

e) (4 pts) What were your results (p-value calculation), include the details about how many runs of the simulation, what youisolated and any math that you did f) (4 pts) What do you conclude based on your p-value? (with respect to both the null and the research hypothesis)

g) (3 pts) Assuming our alpha level is 5% what is the probability that we have committed a Type I error?

h) (3 pts) Assuming our alpha level is 5%, could we have committed a Type II error?