At t = 0s, the leading edge of a wave (wavelength 1m) is 3m to the left of a boundary. The wave is moving to the right at 1m/s. The transmitted wave has wavelength 3m. (You may draw pictures to help you answer the questions below, but you must explicitly state - in words - the answers to the questions.)

(a)[8 pt(s) ]At t = 5s, where is the leading edge of the transmitted wave? Is the transmitted wave inverted or non-inverted, and why?

The Cheebles cookie factory changed their recipe. The inspectors took a sample of the new cookies and found that the sample was 42 grams with a standard deviation of 4 grams. the Cheebles CEO specially asked the inspectors to use these statistics to find the lower and upper boundary weighs of 50% of their cookies. What are the Z values of the limits of the limits of the area covering the middle half of the area under the normal curve that the inspectors would use to find this information for the CEO of Cheebles?

In the city of Urbanville, land is divided between supermarkets and houses (for residents). There is a train station at x = 0.

- Urbanville residents all work from home. Their utility of living in the city is U = 20 − R, where R is the rent they pay. These residents also have the option of moving out of the city and living far away from Urbanville. Doing so gives them a utility of U₀ = 18.

- Supermarkets receive goods from the central train station. Their profits are π = P_g − 2d − R. In the profit equation, d stands for the distance to the train station.

- The price of groceries is P_g= 10.

(a) Draw the bid rent curves for supermarkets and houses (b_s and b_h).

(b) Find x* , such that land from 0 to x* is used for supermarkets and land farther away than x* is used for houses.
(c) Draw the new bid-rent curve for supermarkets (b'_s ) and find x₁, the new boundary between supermarkets and houses.

Transportation costs fall, such that supermarket profits are now given by π' = P_g − d − R.

(d) On the same diagram as before, draw the new bid-rent curve for supermarkets (b'_s ) and find x1, the new boundary between supermarkets and houses.

Q2.

(a) What are the differences between an energy based ligand design method such as GRID and a
knowledge based one like LUDI? What are the requirements of a knowledge based ligand design
method?

(b) Interpret the following QSAR equation: log (1/C)=k 1 ?-k 2 ? 2 + k 3 ?. How are factorial design
methods using in QSAR compound selection? Briefly outline how multiple linear regression analysis is
used in the derivation of a QSAR equation. How is cross-validation used for checking the quality of a
regression based QSAR model?

Q3.

(a) Use the example of molecular docking of the antibiotic netropsin to DNA to distinguish
quantitatively the differences between steepest descent and conjugate gradient methods for initial
refinement and stringent minimization. What qualitative conclusions can be drawn about the efficacy
of these two minimization techniques with respect to this docking experiment?

(b) Using two
examples, explain the thermodynamic differences between the Molecular Dynamics and Monte Carlo
methods. What are the advantages to choosing periodic boundary conditions in ANY molecular
simulation of a macromolecule? Use a diagram to plot 4 such periodic cell shapes. What important
class of applied molecular simulations have benefitted from the usage of periodic boundary

Data from 1991 General Social Survey classify a sample of Americans according to their gender and their opinion about afterlife (example from A. Agresti, 1996, “Introduction to categorical data analysis”). The opinions about afterlife were classified into two categories: Yes and No (or undecided). For example, for the females in the sample - 435 said that they believed in an afterlife and 147 said that they did not or were undecided.

Estimate the proportion of females who believed in an afterlife (Use a 95% Confidence Interval).

Test hypothesis that the majority of females (that is, more than 50% females) believed in an afterlife.

- Using a z-score test

Using c² test

The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The population mean is thought to be 100, and the population standard deviation σ is 2. You wish to test H0 : µ = 100 versus H1 : µ 6= 100. Note that this is a two-sided test and they give you σ, the population standard deviation. (a) State the distribution of X¯ assuming that the null is true and n = 9.

(b) Find the boundary of the rejection region for the test statistic (these critical values will be z-values) if the type I error probability is α = 0.01.

(c) Find the boundary of the rejection region in terms of ¯x if the type I error probability is α = 0.01. In other words, how much lower than 100 must X¯ be to reject and how much higher than 100 must X¯ be to reject. You will have an ¯xlow and an ¯xhigh defining the rejection region. HINT: You are un-standardizing your z from part (b) here.

(d) What is the type I error probability α for the test if the acceptance region for the hypothesis test is instead defined as 98.5 ≤ x¯ ≤ 101.5? Recall that α is the probability of rejecting H0 when H0 is actually true.

Non-Parametric Tests

Complete each part and then put together a finalized report (Word document) of your findings. Copy/Paste any tables, Excel formulas, etc. in an appendix at the end of the document.

Part I - Do Students Really Cheat?

In a recent poll, 400 students were asked about their experiences with witnessing academic dishonesty among their classmates. Suppose 172 students admitted to witnessing academic dishonesty, 205 stated they did not and 23 had no opinion. Use the sign test and a significance of 0.05 to determine whether there is a difference between the number of students that have witnessed academic dishonesty compared to those that have not.

Part II – Is There Really a Difference in Studying vs. “Obtaining Answers”

Salaries were collected by recent graduates that were placed in groups that either admitted to dishonesty during college or they were honest the entire degree. We wish to test if after graduation their salaries are the same or if there is a difference in their salaries? Use a level of significance of 0.10. Be sure to clearly state what you are testing as well as interpret your final results.

The data is as follows:

Year    Name    MinPressure_before      Gender_MF       Category        alldeaths
1950    Easy    958     1       3       2
1950    King    955     0       3       4
1952    Able    985     0       1       3
1953    Barbara 987     1       1       1
1953    Florence        985     1       1       0
1954    Carol   960     1       3       60
1954    Edna    954     1       3       20
1954    Hazel   938     1       4       20
1955    Connie  962     1       3       0
1955    Diane   987     1       1       200
1955    Ione    960     0       3       7
1956    Flossy  975     1       2       15
1958    Helene  946     1       3       1
1959    Debra   984     1       1       0
1959    Gracie  950     1       3       22
1960    Donna   930     1       4       50
1960    Ethel   981     1       1       0
1961    Carla   931     1       4       46
1963    Cindy   996     1       1       3
1964    Cleo    968     1       2       3
1964    Dora    966     1       2       5
1964    Hilda   950     1       3       37
1964    Isbell  974     1       2       3
1965    Betsy   948     1       3       75
1966    Alma    982     1       2       6
1966    Inez    983     1       1       3
1967    Beulah  950     1       3       15
1968    Gladys  977     1       2       3
1969    Camille 909     1       5       256
1970    Celia   945     1       3       22
1971    Edith   978     1       2       0
1971    Fern    979     1       1       2
1971    Ginger  995     1       1       0
1972    Agnes   980     1       1       117
1974    Carmen  952     1       3       1
1975    Eloise  955     1       3       21
1976    Belle   980     1       1       5
1977    Babe    995     1       1       0
1979    Bob     986     0       1       1
1979    David   970     0       2       15
1979    Frederic        946     0       3       5
1980    Allen   945     0       3       2
1983    Alicia  962     1       3       21
1984    Diana   949     1       2       3
1985    Bob     1002    0       1       0
1985    Danny   987     0       1       1
1985    Elena   959     1       3       4
1985    Gloria  942     1       3       8
1985    Juan    971     0       1       12
1985    Kate    967     1       2       5
1986    Bonnie  990     1       1       3
1986    Charley 990     0       1       5
1987    Floyd   993     0       1       0
1988    Florence        984     1       1       1
1989    Chantal 986     1       1       13
1989    Hugo    934     0       4       21
1989    Jerry   983     0       1       3
1991    Bob     962     0       2       15
1992    Andrew  922     0       5       62
1993    Emily   960     1       3       3
1995    Erin    973     1       2       6
1995    Opal    942     1       3       9
1996    Bertha  974     1       2       8
1996    Fran    954     1       3       26
1997    Danny   984     0       1       10
1998    Bonnie  964     1       2       3
1998    Earl    987     0       1       3
1998    Georges 964     0       2       1
1999    Bret    951     0       3       0
1999    Floyd   956     0       2       56
1999    Irene   987     1       1       8
2002    Lili    963     1       1       2
2003    Claudette       979     1       1       3
2003    Isabel  957     1       2       51
2004    Alex    972     0       1       1
2004    Charley 941     0       4       10
2004    Frances 960     1       2       7
2004    Gaston  985     0       1       8
2004    Ivan    946     0       3       25
2004    Jeanne  950     1       3       5
2005    Cindy   991     1       1       1
2005    Dennis  946     0       3       15
2005    Ophelia 982     1       1       1
2005    Rita    937     1       3       62
2005    Wilma   950     1       3       5
2005    Katrina 902     1       3       1833
2007    Humberto        985     0       1       1
2008    Dolly   963     1       1       1
2008    Gustav  951     0       2       52
2008    Ike     935     0       2       84
2011    Irene   952     1       1       41
2012    Isaac   965     0       1       5
2012    Sandy   945     1       2       159
                                        

Open Hurricane data.

SETUP: Is it reasonable to assume that average hurricane pressure for category 4 is different from that of category 1? Given the data, your job is to check if this assertion is indeed reasonable or not. HINT: Read Lecture 24.

19. What would be the correct Null-Hypothesis?

• a. Data related to two different categories should not be related.
• b. The population averages are equal.
• c. The slope of the regression line is equal to zero.
• d. None of these.

20. The P-value is 3.33E-09. What can be statistically concluded?

• a. We reject the Null Hypothesis.
• b. We accept the Null Hypothesis.
• c. We cannot reject the Null Hypothesis.
• d. None of these.

21. Write a one-line additional comment.

• a. We cannot conclude that data related to two different hurricane categories are related.
• b. We are confident that hurricanes with category 4 has different pressure than those of category 1.
• c. We cannot conclude that hurricanes with category 4 has lower pressure than those of category 1.
• d. None of these.

Year    Name    MinPressure_before      Gender_MF       Category        alldeaths
1950    Easy    958     1       3       2
1950    King    955     0       3       4
1952    Able    985     0       1       3
1953    Barbara 987     1       1       1
1953    Florence        985     1       1       0
1954    Carol   960     1       3       60
1954    Edna    954     1       3       20
1954    Hazel   938     1       4       20
1955    Connie  962     1       3       0
1955    Diane   987     1       1       200
1955    Ione    960     0       3       7
1956    Flossy  975     1       2       15
1958    Helene  946     1       3       1
1959    Debra   984     1       1       0
1959    Gracie  950     1       3       22
1960    Donna   930     1       4       50
1960    Ethel   981     1       1       0
1961    Carla   931     1       4       46
1963    Cindy   996     1       1       3
1964    Cleo    968     1       2       3
1964    Dora    966     1       2       5
1964    Hilda   950     1       3       37
1964    Isbell  974     1       2       3
1965    Betsy   948     1       3       75
1966    Alma    982     1       2       6
1966    Inez    983     1       1       3
1967    Beulah  950     1       3       15
1968    Gladys  977     1       2       3
1969    Camille 909     1       5       256
1970    Celia   945     1       3       22
1971    Edith   978     1       2       0
1971    Fern    979     1       1       2
1971    Ginger  995     1       1       0
1972    Agnes   980     1       1       117
1974    Carmen  952     1       3       1
1975    Eloise  955     1       3       21
1976    Belle   980     1       1       5
1977    Babe    995     1       1       0
1979    Bob     986     0       1       1
1979    David   970     0       2       15
1979    Frederic        946     0       3       5
1980    Allen   945     0       3       2
1983    Alicia  962     1       3       21
1984    Diana   949     1       2       3
1985    Bob     1002    0       1       0
1985    Danny   987     0       1       1
1985    Elena   959     1       3       4
1985    Gloria  942     1       3       8
1985    Juan    971     0       1       12
1985    Kate    967     1       2       5
1986    Bonnie  990     1       1       3
1986    Charley 990     0       1       5
1987    Floyd   993     0       1       0
1988    Florence        984     1       1       1
1989    Chantal 986     1       1       13
1989    Hugo    934     0       4       21
1989    Jerry   983     0       1       3
1991    Bob     962     0       2       15
1992    Andrew  922     0       5       62
1993    Emily   960     1       3       3
1995    Erin    973     1       2       6
1995    Opal    942     1       3       9
1996    Bertha  974     1       2       8
1996    Fran    954     1       3       26
1997    Danny   984     0       1       10
1998    Bonnie  964     1       2       3
1998    Earl    987     0       1       3
1998    Georges 964     0       2       1
1999    Bret    951     0       3       0
1999    Floyd   956     0       2       56
1999    Irene   987     1       1       8
2002    Lili    963     1       1       2
2003    Claudette       979     1       1       3
2003    Isabel  957     1       2       51
2004    Alex    972     0       1       1
2004    Charley 941     0       4       10
2004    Frances 960     1       2       7
2004    Gaston  985     0       1       8
2004    Ivan    946     0       3       25
2004    Jeanne  950     1       3       5
2005    Cindy   991     1       1       1
2005    Dennis  946     0       3       15
2005    Ophelia 982     1       1       1
2005    Rita    937     1       3       62
2005    Wilma   950     1       3       5
2005    Katrina 902     1       3       1833
2007    Humberto        985     0       1       1
2008    Dolly   963     1       1       1
2008    Gustav  951     0       2       52
2008    Ike     935     0       2       84
2011    Irene   952     1       1       41
2012    Isaac   965     0       1       5
2012    Sandy   945     1       2       159
Test if there is a significant difference in the death by Hurricanes and Min Pressure measured. Answer the questions for Assessment. (Pick the closest answer)

7. What is the P-value?

• a. #DIV/0!
• b. 0.384808843
• c. 0.634755682
• d. None of these

8. What is the Statistical interpretation?

• a. The P-value is too large to have a conclusive answer.
• b. The P-value is too small to have a conclusive answer.
• c. ​​The P-value is much smaller than 5% thus we are certain that the average of hurricane deaths is significantly different from average min pressure.
• d. None of the above.

9. What is the conclusion?

• a. The statistics does not agree with the intuition since one would expect that stronger hurricanes to be deadlier.
• b. ​​Statistical interpretation agrees with the intuition, the lower the pressure the stronger the hurricanes.
• c. Statistics confirms that hurricanes’ pressure does relate to the death count.
• d. The test does not make statistical sense, it compares “apples and oranges”.