FOR ALL QUESTIONS PLEASE USE THE SCENARIO BELOW:

In order to compete in the saturated energy drink market, the company Boost developed an energy drink recipe called Over 9000, claiming that a smaller proportion of people who consume it experience crashes (sudden decreases in energy levels) than other energy drinks. It's generally accepted that energy drink consumption, generally speaking, is associated with crashes in 33% of people, and new energy drinks are assumed to have this property as well. Boost's totally honest research team conducted an experiment and concluded that 31 out of 100 participants who drank Over 9000 experienced a crash. Of course 31% is less than 33%, but is Boost's claim statistically justified? Let's find out by conducting a hypothesis test.

3. The alternative hypothesis would be of the form...

a. parameter > number

b. parameter number

c. parameter < number

5. What are some of the possible consequences in making the two types of statistical errors in this context? Be very clear in distinguishing the types of errors and their consequences.

7. For each of the assumptions for this one proportion hypothesis test (listed below), discuss whether or not the assumptions are met. Express your answer as "yes, because...", "no, because...", or "we can't tell, but we could do... to find out" (fill in the ...s).

1. There is a fixed number of individuals in the sample.
2. The individuals form a simple random sample from a relevant population.
3. The variable of interest has two possible outcomes.
4. Whether or not the variable of interest is a success or not is independent from individual to individual.
5. np5 and nq5

8. The research team chose a significance level of =0.05and ultimately found a p-value of 0.07. What would their statistical conclusion be?

a. Accept the null hypothesis

b. Fail to reject the null hypothesis

c. Reject the null hypothesis

9. State their statistical conclusion in the context of the problem in a practical way with more normal words.

10. Which of the following confidence intervals is the most likely to be true given the p-value above?

a. (0.88, 0.98)

b. (0.27, 0.37)

c.(0.35, 0.45)

d. (0.31, 0.41)

e. (0.02, 0.12)

11. Interpret your chosen confidence interval (a) statistically, then (b) using real-world terminology.