Suppose you have two strains of mice, S1 and S2. Strain S2 is genetically modified to metabolize a pharmacon P supposedly faster than S1. You conducted an experiment in a sample set of each strain, in which the pharmacon was injected and its concentration in blood was measured every 15min for 2h. Of course, age, gender, and weight was recorded for each animal. You want to statistically demonstrate that the metabolic rate of N is higher in S2 than S1. For simplicity, let us assume that the pharmacon is metabolized by a 0th order (linear) kinetic.

1. Describe a statistically correct and efficient approach for analyzing the data.

2. Which statistical model is suitable to address the question above? Explain how this model works and how results are interpreted.

3. A few animals die (e.g., due to toxic effects) during the experiment. How would you deal with this problem in the statistical analysis?

The following three columns of data represent observations (number of aphids killed per m²) following three pesticide treatments (A-C), with each treatment being “replicated” five times.

Analyse the strength of evidence for a treatment effect (A-C) if:

1. the experiment was completely randomised (i.e. rows have no meaning)

and alternatively if:

2. the experiment was in randomised spatial blocks, with observations from the same block being in the same row (i.e. 5.1, 5.7, 6.5 block 1; 8.2, 6.3, 8.1 block 2…). In this case the rows have meaning.

Why do you come to different conclusions about the effects of pesticide dependent on the method applied? In each instance, please provide a statement of the null hypotheses and alternates, the fitted equation, a qualitative summary of whether the model assumptions are met, and a conclusion

(10) 2. ESP (extra sensory perception) is the ability to read minds. We have a set of cards with each card having one of 5 shapes on them (square, rectangle, triangle, circle, question mark) and there are an equal number of each shape in the deck. We are going to select one card from the deck, stare at it and then there is a guy who claims he has ESP who is going to guess at the shape on the card we drew out (after each time we pull a card out – the ESP dude will make a guess- then we put the card back ). We did this experiment 250 times and we count how many times he guesses correctly

a) Why does this an experiment that fits the criterion of a binomial?

b) What is the mean, standard deviation and normal range for the number of times he guesses correctly

c) If he guesses 55 correct do you think he has ESP? Explain

An automobile manufacturer claims that its cars average more than 410 miles per tankful (mpt).
As evidence, they cite an experiment in which 17 cars were driven for one tankful each and
averaged 420 mpt. Assume σ = 14 is known.

a. Is the claim valid? Test at the 5 percent level of significance.

b. How high could they have claimed the mpt to be? That is, based on this experiment, what is the maximum value for µ which would have been rejected as an hypothesized value?

c. What is the power of the test in part (a) when the true value of µ is 420 mpt? (Hint: Your rejection region for part (a) was stated in terms of comparing Zobs with a cut-off point on the Z distribution. Find the corresponding x̅cut-off and restate your rejection region in
terms of comparing the observed x̅value with the x̅cut-off. Then assume H1 is true (i.e. µ
= 420 mpt) and find the probability that x̅is in the rejection region.)

     I-Multiplication Rules

1. How many different slats can be made. If the splint is composed of 4 letters and 3 digits.

2. How many special shuttle crews can be formed if: for pilot position, co-pilot and flight engineer there are (8) eight candidates, for two scientists one for solar experiment and one for stellar experiment there are (6) candidates and for two Civilians there are (9) candidates.

II-permutations and combinations

1. In a raffle where there are 10 possible numbers in each ball, if three pellets are extracted. How many ways is it possible to combine extracted numbers?

2. Ten people reach a row at the same time. How many ways can they be formed?

3. In a Olympiad there are 10 swimmers in a race, how many ways can arrive the first three places?

4. How many committees of three teachers can be made if there are 6 teachers to choose from?

For this task you will examine the experiments of Loftus and Gardner. Describe and analyze each of these experiments. You will prepare two separate analyses; for each analysis, include the following:

A brief summary of the study

A one paragraph explanation of   the background in the field leading up to the study, and the reasons the researchers carried out the project.

The significance of the study to the field of psychology

A brief discussion of supportive or contradictory follow-up research findings and subsequent questioning or criticism from others in the field  

A summary of at least one recent experiment (within the past two years) that is related to the seminal experiment (Hint: Excellent sources for recent research summaries are the American Psychological Association’s Monitor on Psychology and the Association for Psychological Science).

Your own evaluation of whether the breakthrough experiments of Drs. Gardner and Loftus were examples of genius, the zeitgeist, or some other factor. Use their own autobiographical accounts as well as your analyses of their experiments and personal stories to support your opinion.

Robert Millikan is famous for his experiment which demonstrated that electric charge is discrete, or quantized. His experiment involved measuring the terminal velocities of tiny charged drops of oil in air between two plates with a known voltage applied. He timed hundreds of them traveling both up and down in order to mathematically rule out the effects of gravity and drag, since he had no way of measuring mass or diameter. His results showed that charge comes only in integer multiples of 1.6 10 19C. This is called the elementary charge. It is the charge on both electrons, negative, and protons, positive.
1. a. Where does charge excess charge reside on an object? Why?
b. Where is electric charge more concentrated on irregularly shaped objects?
c. How do lightning rods work?
d. Why does a stream of water bend toward a charged object?
e. What are the three methods of charging an object?

In problems 1 – 5, a binomial experiment is conducted with the given parameters. Compute the probability of X successes in the n independent trials of the experiment.

1.         n = 10, p = 0.4, X = 3

2.         n = 40, p = 0.9, X = 38

3.         n = 8, p = 0.8, X = 3

4.         n = 9, p = 0.2, X < 3

5.         n = 7, p = 0.5, X = > 3

According to American Airlines, its flight 1669 from Newark to Charlotte is on time 90% of the time. Suppose 15 flight are randomly selected and the number of on – time flights is recorded.

            a.         Find the probability that exactly 14 flights are on time.

            b.         Find the probability that at least 14 flights are on time.

            c.          Find the probability that fewer than 14 flights are on time.

            d.         Find the probability that between 12 and 14 flights are on time.

            e.         Find the probability that every flight is on time.

Even if the double slit experiment gives interesting (weird) results, it only concludes that each photon interacts with itself after passing the two slits. I have been thinking about a different experimental setup, where you have two well defined light sources (with specific wave lengths and phase) but no slits. And now to my questions: Has anyone ever done such an experiment, and will there be an interference pattern on the wall?

If the answer to the second question is "no", light can not be a true wave - it only has some wavelike properties. But if it is "yes", things become much more interesting.

If there is an interference pattern on the wall, there has to be an interference pattern even if both light sources are emitting single photons at random, but as seldom as, say, once per minute. That in turn would mean that the photons know about each other, even if they are separated in time with several seconds, and the light sources are independent (not entangled).

Consider the Monty Hall problem.Verify the results using by writing a computer program that estimates the probabilities of winning for different strategies by simulating it.

1. First, write a code that randomly sets the prize behind one of three doors and you also randomly select one of the doors. You win if the the door you selected has the prize (Here, we are simulating ’stick to the initial door’ strategy). Repeat this experiment 100 times and compute the average number of wins.

2. Next, try simulating the switching strategy. Find the door the host will open and change your initial door with the door not opened by the host. Also repeat this experiment 100 times and compute the average number of wins. If you did everything right, the first code should yield the probability of winning as ≈ 1/3 and the second code should yield ≈ 2/3. You can use any programming language you want (MATLAB, Python etc.)