Briefly describe how you would test your hypotheses, including data collection methods and statistical analysis. (Max. length: 100 words)

Define the population of interest and the unit of analysis.

Based on the research goal and proposed variables, formulate one clear, testable research hypothesis.

LuxuryStay hotels is considering introducing an early check-in option, allowing guests to access their rooms before the standard check-in time. However, the hotel chain is uncertain about this strategy's impact on guest behavior and bookings.

Your task is to draft a research plan to assess the impact of the early check-in option.

In a random experiment, event A occurs with probability 0.2. The experiment is carried out 3 times independently. The random variable X is defined as: X = "Number of the times that A occurred in the 3 independent tests."

What is the expected value and variance of X?

Emily hits 60% of her free throws in basketball games.  If she had 25 free throws in last week's game, what was Emily's expected number of hits?

Ten percent of all college graduates hired stay with the same company for more than five years. In a random sample of six recently hired college graduates, the probability that exactly two will stay with the same company for more than five years is closest to:

A coin is weighted in such a way so that there is a 70% chance of getting a head on any particular toss. Toss the coin, in exactly the same way, 100 times. Let X equal the number of heads tossed. 

Indicate whether the following statement is true or false: "X is a binomial random variable"

Which of these variables do you expect to be uniformly distributed?