A chemical manufacturer has been researching new formulas to provide quicker relief of minor pains. His laboratories have produced three different formulas, which he wanted to test. Fifteen people who complained of minor pains were recruited for an experiment. Five were given formula 1, five were given formula 2, and the last five were given formula 3. Each was asked to take the medicine and report the length of time until some relief was felt. The results below shows the time until relief is Felt.

Formula -1 : 4 8 6 9 8

Formula - 2 : 2 5 3 7 1

Formula - 3 : 6 7 7 8 6

SST = 78.4, SSE=42
(a) Write down the model and the ANOVA table to test whether there exits any differences in the time of relief exist among the three formulas? Use α =0.05.
(b) Is the Formula-1 different from Formula-3 at 5% level

1. If you were creating a library using the restriction endonucleases SbfI and EcoRI, for which restriction site would you design a fork-tailed adapter? Can you imagine any characteristic of a genome that would cause you to design a fork-tailed adapter for the other restriction site? If you were to use this set of enzymes/adapters to create a library in corn, how many reads would you need for adequate coverage of each individual?

2. How many reads would you need using SbfI/EcoRI in zebrafish to provide adequate cover for each individual? How many would you need for a stickleback fish? Does this make sense, given the size of the respective genomes? How could you explain this observation? Does looking at the results for different enzyme combinations for these two species help to explain the observation?

3. How many individuals could you analyze on a single MiSeq run, if you were using the combination of NlaIII and MluCI on mice?

4. If you were interested in doing a study of population structure in corn, which enzyme combination would you choose?  How many individuals could you analyze with a single MiSeq run? How about with a single lane of an Illumina HiSeq 2000?

5. Suppose you were using paired-end sequencing with 250 cycles. How much of the genome of a stickleback fish would you expect to sequence at >7X coverage if you used EcoRI/MspI?

6. You amplify an EcoRI/MspI fragment using MspI 2.1.0 and EcoRI 1.1.0 adapters and the the PCR primers NGS_i5_S505 and NGS_i7_N719. What would the final amplicon look like? (Write the sequence.)  

7. What happens to MspI/MspI fragments in the ddRadSeq protocol we are following? How about EcoRI/EcoRI fragments?

8. We are using three different MspI and EcoRI adapters in our protocol. There are a couple of advantages to using more than one adapter for each end; what are they?

9. Taking into consideration the different indices available, and the use of three different adapters for each end of genomic fragments, how many different individuals could be analyzed with a single sequencing run?

10. Suppose you were analyzing mice just as depicted in Table 1. of Petersen et al., using the enzyme pair EcoRI-MspI  You want to increase the number of fragments you are analyzing by 50%; how would you adjust your protocol?

11. For SNP discovery, there are concerns that ddRadSeq may limit analysis to regions of the genome with low point mutation rates. Please explain why this would be so.

12. Explain the similarities between ddRadSeq and two-step PCR. Why isn’t a PCR step (instead of ligation) used on the genomic fragments in ddRadSeq?

13. If you were using single step PCR, how many different primers would you need to take full advantage of the indices available from Illumina (S502, N701, etc.) for one locus? How many would be needed if you were using two-step PCR for one locus? How would the answers change for 10 loci?

14. What are the advantages of two-step PCR over one-step PCR? Are there any conditions under which one-step PCR is more efficient?

15. A typical number of cycles for the second PCR in two-step PCR is 10. How many copies of each input molecule would be generated in ten cycles?

16. What would happen if you used two-step PCR, and the primers used in the first step were both compatible with i7 primers? Would amplification happen in the second step of the two-step PCR process? Could the amplicon be sequenced?

IRISH CASE STUDY The O’Rourke family lives on a small farm in Iowa and comprises David, aged 30; his wife, Mary, aged 29; and two children: Bridget, aged 7, and Michael, aged 6. Both David and Mary are second-generation Irish. Before purchasing their farm 5 years ago, David sold farm equipment in Ohio. The O’Rourkes are Catholic; Mary converted to Catholicism when they married. 7.Describe the O’Rourke family’s communication patterns. 8.What are the predominant health conditions among Irish immigrants? 9.Explain the significance of the Great Potato Famine for Irish Americans. 10. Name two genetic diseases common among Irish Americans. 11. Identify accepted fertility practices for Irish American Catholics. 12.Identify three sources of strength for the Irish American in times of illness. 13. Identify traditional home remedies commonly used by Irish American

Exercise 5 (15) In the process of learning how to conduct a sign test, each student inevitably punches their computer screen several times. I have found that students who punch their screens during this exercise can be separated into two categories. The first category believes that this statistics course would be better if they did all of their statistics by hand. The second category is pleased that the course is taught using R. Below is the number of times a computer screen is punched by a student in each category. Assume all assumptions have been met.

1. By hand, test the hypothesis that there is no difference between the two categories in relation to how many times they punch their computer screen. Provide the scrap paper used to conduct this test.

2. By hand, calculate the 95% CI of the difference between the means.

Consider a two-step binomial tree for a European put option on a non-dividend paying stock “XY”. The current price of stock “XY” is $60. Over each of the next two 6-month periods the stock price is expected to go up by 10% or down by 10%. The risk-free rate of interest is 8% per annum with continuous compounding. The European put option will expire in 1 year and has an exercise price of $55.

a) Calculate the probabilities that the stock price goes up and down in the risk neutral world. [4 marks]

b) Calculate the stock price at each node of the binomial tree. [7 marks]

c) Use the binomial option pricing formula to calculate the value of the put option at each node of the tree. [12 marks]

d) Can you explain why, in your calculations of the option price, you are allowed to use the risk-free rate of interest? [7 marks]

QUESTION 2

Consider the following four--?step assembly operation with quality problems.

-The first resource has a processing time of 7 minutes per unit and one employee doing the operation

? The second resource has a processing time of 4 minutes per unit.  It also has one employee doing the operation. However, this is a very delicate task and 0.79 of all products have to be scrapped after this step.

? Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 17minutes per unit.

? At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

What is the process capacity per hour? (keep two decimal)

Franklin purchases 40 percent of Johnson Company on January 1 for $604,600. Although Franklin did not use it, this acquisition gave Franklin the ability to apply significant influence to Johnson’s operating and financing policies. Johnson reports assets on that date of $1,518,000 with liabilities of $598,000. One building with a seven-year remaining life life is undervalued on Johnson’s books by $311,500. Also, Johnson’s book value for its trademark (10-year life) is undervalued by $280,000. During the year, Johnson reports net income of $112,000 while declaring dividends of $50,000. What is the Investment in Johnson Company balance (equity method) in Franklin’s financial records as of December 31?

a. $618,200.

b. $600,400.

c. $629,400.

d. $645,200.

Franklin purchases 40 percent of Johnson Company on January 1 for $601,700. Although Franklin did not use it, this acquisition gave Franklin the ability to apply significant influence to Johnson’s operating and financing policies. Johnson reports assets on that date of $1,554,000 with liabilities of $582,000. One building with a seven-year remaining life life is undervalued on Johnson’s books by $222,250. Also, Johnson’s book value for its trademark (10-year life) is undervalued by $310,000. During the year, Johnson reports net income of $96,000 while declaring dividends of $40,000. What is the Investment in Johnson Company balance (equity method) in Franklin’s financial records as of December 31?

A) $599,000

B) $637,400

C) $611,700

D) $624,100