Please read of the questions carefully and show your work to the best of your ability.

You must state any assumptions for tests you do, also do preliminary work to show that you tested them. You may assume an alpha level of 0.05 for all questions that ask about statistical significance.

1. 1. Intergalactic scientists recruited by the Rebellion were tasked with studying midi-chlorian levels in children and young adults (aged 5 to 25). Midi-chlorian counts are linked to sensitivity to The Force and may confer extraordinary abilities. Normal "Human" midi-chlorian levels average approximately 2,500 per cell and much higher levels of midi-chlorian are observed in Jedi. Using a large and random sample, these scientists determine that the standard deviation of mid-chlorian counts is approximately 625 per cell. These Rebel Scientists wish to identify individuals with sufficient Force sensitivity (i.e., potential to be trained as new Jedi) and have declared that for now, only Humans with a z-score of at least 2.4 may qualify.

a)What is the minimum mid-chlorian count that would be classified as being sufficiently Force-sensitive?

b) What proportion of the Human population can potentially be trained as new Jedi?

c) Midi-chlorian counts lower than 2,000 provide no sensitivity to the Force. What proportion of the Human population are therefore useless to train for the Jedi Order?

d) What assumptions must the Rebels make for these data to be accurate?

2. A new study published in the esteemed New Republic Journal of Medicine reported results from a randomized trial designed to assess the effect of a drug calledbota on boosting the effects of midi-chlorians to enhance a Human's Force-sensitivity. The study reports a model including bota as a binary variable calledExposure that indicates treatment with the drug (0 = no; 1 = yes), gender as a binary variable calledFemale(0 = male; 1 = female), age in years, and the number of servings of fruits consumed per day. The dependent variable is defined as enhanced Force-sensitivity (0 = no; 1 = yes).

a) Write the complete regression equation for the model provided above.

b) Interpret the number in the "odds ratio" column for the variableExposure in one sentence.

c) Interpret the number in the "odds ratio" column for the variableFruits in one sentence. d) The value represented by the letterA is (please bold / highlight / or somehow indicateyour answer choice):

Less than 0

Greater than 0

This information cannot be determined from the data provided

The value represented by the letterBis (please bold / highlight / or somehow indicateyour answer choice):

Less than 0

Greater than 0

This information cannot be determined from the data provided

Do you think that the Rebel Scientists should give bota to Humans to enhance their Force-sensitivity? In no more than two sentences, report why or why not.

3. Given the paucity of Force-sensitive Humans, Rebel Scientists begin to consider environmental factors that might be associated with diminished midi-chlorian counts. Several chemicals were evaluated. There was particular interest in assessing serum levels of the element Fermium, a heavy metal that does not occur naturally. Below are linear regression output for fermium followed by questions.

a) Quantify the relationship between fermium and midi-chlorian count in one sentence.

b) What can you say, if anything, about the correlation coefficient between serum Fermium and midi-chlorian count?

c) If a randomly selected Human has a serum Fermium level 10 units lower than their neighbor, what is the best prediction for their difference in midi-chlorian count?

d)Interpret the _cons term.

Although not shown, you are told that the R² for the model above is 0.17.

e) What does this mean?

f) Given this information, how would you advise the Rebel Scientists with respect to next steps?

4.4. Suppose that the Rebel Scientists further adjusted their simple model from the previous question (i.e., the model in Question 3 above assessing the association between serum Fermium and midi-chlorian counts) for age, gender, and family history of Force-sensitivity (0 = no; 1 = yes).

a)Write the full multivariable regression model.

b) They found that the coefficient for "family history" was 10.26 (95% confidence interval: 7.13 to 13.38, p = 0.0003). Interpret the slope and define the p-value and 95%CI.

c) The R² for the new multivariable model is 0.57. In no more than two sentences: 1) interpret this statistic; and 2) comment on the difference from the R² of 0.17 that was reported for the simple model.

d) Imagine that you asked the Scientists why they decided to focus on Fermium, and the team replied that they simply tested every element from the periodic table to see what was related to midi-chlorian counts. In no more than two sentences, tell me: 1) what statistical topic would immediately come to your mind; and 2) what would you say to the Rebel Scientists?