Happy the elf (who is a male elf) tells you that one of the reasons he’s so happy is that the sex ratio of elves working at the North Pole is “two girls for every boy”2 . Slartibartfast, another elf, claims that Happy’s name should be “Delusional” because the proportion of female elves is much lower than Happy claims. You decide to test Happy’s claim by simply tallying the sex of each of the next 100 elves who walk by you on their way to work. How many male elves out of the 100 would it take for you to reject (at α = .05) Happy’s claim and find in favour of Slartibartfast? Show how you have calculated your answer.

After a campaign to encourage students to take precautions against skin cancer, in a certain high school class consisting of 34 girls and 39 boys, it is observed that 26 girls and 25 boys take precautions as measured by a survey to elicit how often they wear sunscreen, sunglasses and hats for protection against the sun.

Please use this information to calculate the probabilities for the following questions. Please provide each numerical answer to TWO DECIMAL places (X.XX) with no additional information in the answer box. Just X.XX (i.e. no extra spaces, no units, etc).

What is the probability that a student picked at random takes precautions against skin cancer (by wearing sunscreen, sunglasses and a hat), given that the student is a boy?

The Titanic Used the data in the following table, which summarizes results from the sinking of the titanic.

1. If one of the Titanic passengers is randomly selected, find the probability of getting someone who is a women or survivor.
2. If one of the Titanic passengers is randomly selected, find the probability of getting a man and someone who survived the sinking.
3. If one of the Titanic passengers is randomly selected, find the probability of getting a boy or girl?
4. If one of the Titanic passengers is randomly selected, find the probability of getting a man, given that the selected person died.
5. If Three of the Titanic passengers is randomly selected, find the probability of all three are boys?

Summary of DIRTY HARRY CLIP
In the Dirty Harry clip, Harry tortures the guy by shooting him in the leg to obtain information on where the girl was.  Cop Harry Callahan (Clint Eastwood) attempts to track down a psychopathic rooftop killer before a kidnapped girl dies. When he is found Harry abuses the murderer's civil rights putting him back on the streets. Once he is released he hijacks a school bus and Harry must go after him again. The only way to stop this vicious killer is in cold blood.

NOW ANSWER THE FOLLOWING QUESTIONS AGREEING HOW ITS NOT OKAY TO TORTURE TO AQUIRE INFORMATION OR CONFESSIONS

Given a life or death situation (as in Dirty Harry),
-Explain why its not justified for police officers to use torture or other means to obtain information from a suspect to save a life?
-When would it be acceptable and when would it not be acceptable?
-Or, should officers never use any means necessary to obtain a confession and always follow the law and protect the Constitutional rights of an accused?

2. Suppose that there is a drug that was shown to be effective at treating the novel coronavirus. Only two firms can produce this drug. The (inverse) demand function for the drug is given by P = 200 − 2Q where Q is the quantity of the drug available in the market and P is the market price. Firm 1 produces the drug with a constant marginal cost of 8 USD (total costs are equal to 8Q for firm 1) while firm 2 produces the drug with a constant marginal cost of 10 USD (total costs are equal to 10Q for firm 2).

a) Define the best response functions of each firm.

b) Find the equilibrium quantities of each firm and find the market price at the equilibrium.

c) Now assume a third firm has figured out how to produce the drug. What do you think will happen to equilibrium quantity and price (answer verbally)?

Question: Company X uses fermentation to produce a valuable industrial chemical. A startup company approaches X with a novel microbe that will increase the yield of the chemical, so that profits will increase by an estimated $14.0k/mo. The startup company wishes to sell the rights to use the microbe for a seven-year period, at a price of $480k.

Engineers at company X estimate the increased production will entail additional maintenance, costing $12.0k in year 2, $14.0k in year 4, and $17.0k in year 6 of the project.

1. What would a cash flow diagram of the project, from the standpoint of Company X?

2. How can I calculate the present value of the project, assuming a 13.0% annual interest rate?

3. Using Excel, make a well-formatted graph of the project present value vs. interest rate, for interest rates ranging from 0 to 30% APR.

"You have developed a new anti-anxiety drug and are interested in its efficacy. You have two groups of rats (N=20 per group). You inject the one group (group 0) with saline, and inject the other group (group 1) with your anti-anxiety drug. Your outcome variable is the amount of exploratory behaviour (‘locomotion’) measured in a novel environment (a mild stress) over 1 hour. "

I ran an independent-samples t-test in SPSS (a statistics program) on this data and the same test but with bootstrapping.

Somehow the results were that the data is insignificant with a p-value of 0.139, alpha of 0.05, but the 95% confidence interval was 6.967 - 61.128.

If the data is insignificant, should 0 not be a value within the 95% confidence interval?

How is it possible that the null value (0) is not within the confidence interval, but still have a rather large insignificant result?

Researchers investigating temperament in dogs have a database of reactivity scores from a population of N = 1000 puppies.  The reactivity scores are normally distributed with a mean of mu = 175 and a standard deviation of sigma = 20; higher scores indicate higher reactivity (that is, the puppy is more likely to become aroused by novel stimuli).

Dr. Kobe is also conducting temperament testing, but his local shelter is much smaller than Dr. Santos’.  Thus, he is only able to obtain a sample size of n = 20 puppies.

a. What is the likelihood that Dr. Kobe will obtain a mean reactivity score of 168 or lower?

b. What is the likelihood that Dr. Kobe will obtain a mean reactivity score of 190 or higher?

c. Why should the probability of obtaining a sample mean less than M = 165 be larger for Dr. Kobe than Dr. Santos?

The Covid-19 coronavirus first struck in Wuhan, the capital of China’s Hubei province, at the end of 2019. It quickly spread beyond Asia. The policy responses have mostly been lockdowns of varying intensities and durations. Though there have been many national and even international curfews in the past, perhaps most prominently during the Second World War, there are no examples of lockdowns on a global scale deployed to counter the spread of disease. It is wholly novel to force significant proportions of the populations of the major world economies to stay at home, and mostly indoors. An important observation by economists is the interplay of demand and supply for personal protective equipment (PPE). With relevant facts and figures, you are required to
1. Identify and explain 5 determinants of demand for PPE.
2. Discuss 5 determinants of PPE supply.
3. Explain any two consequences of a shortage in the supply of PPE.

1A. Look at these particular goods and determine whether it most likely describes perfect competition or monopolistic competition

1. designer dress
2. pears
3. mystery novel
4. wheat
5. milk
6. TV show
7. microwave

1B. Consider the following scenarios and describe how the monopolistic competitor would be impacted in the short run and the long run. Will there be economic profits or economic losses? What will happen to prices after entry or exit? What will economic profits be in the long run?

1. Romantic movies are less popular with the general public.
2. More people are interested in antique furniture.
3. There is much more interest in eating healthier foods.
4. Less people are listening to rock music.
5. Less people are eating at steakhouses.
6. More people are signing up for gym memberships.

1C. Which of the following industries would be described as an oligopoly?

1. Fast-food restaurants
2. Airline industry
3. Bookstore
4. Fashion boutique