Shrewsbury Herbal Products, located in central England close to the Welsh border, is an old-line producer of herbal teas, seasonings, and medicines. Its products are marketed all over the United Kingdom and in many parts of continental Europe as well. Shrewsbury Herbal generally invoices in British pound sterling when it sells to foreign customers in order to guard against adverse exchange rate changes. Nevertheless, it has just received an order from a large wholesaler in central France for £320,000 of its products, conditional upon delivery being made in three months’ time and the order invoiced in euros. Shrewsbury’s controller, Elton Peters, is concerned with whether the pound will appreciate versus the euro over the next three months, thus eliminating all or most of the profit when the euro receivable is paid. He thinks this an unlikely possibility, but he decides to contact the firm’s banker for suggestions about hedging the exchange rate exposure. Mr. Peters learns from the banker that the current spot exchange rate in €/£ is €1.4537; thus the invoice amount should be €465,184. Mr. Peters also learns that the three-month forward rates for the pound and the euro versus the U.S. dollar are $1.8990/£1.00 and $1.3154/ €1.00, respectively.

1) What is the inherent issue or problem in this case? Describe the issue or problem with no more than two sentences.

2) If you were Mr. Peters, what would you do? Answer the following 6 questions.

a. Action or no action?

b. If the decision is no action, describe the problem. What is the term in Finance for this kind of decision?

c. If there is an action, you will engage in a three-month forward contract. What is the term in Finance for this kind of decision.

d. What position would you take if you decide to engage in the forward contract in c).

e. Plot the profit (or loss) profile for your position in the 3-month forward contract. You have to show graphically the relationship between unanticipated changes in the spot exchange rate in 3 months and gains (or losses) of your position on the 3-month forward contract.

f. Draw the outcomes of b) and c) on a graph with the horizontal axis (possible future spot exchange rates in 3 months) and vertical axis (£ value of € receivables).

A consumer advocacy group published a study of labeling of seafood sold in three U.S. states. The study found that 15 of the 25 ​"red snapper" packages tested were a different kind of fish. Assume that the study used a simple random sample. Complete parts a through c below. ​

a) Are the conditions for creating a confidence interval​ satisfied? Explain.

A. ​Yes, because the sample is a simple random​ sample, the sample proportion is between​ 10% and​ 90%, and there are at least 20 expected​ "successes" and 20 expected​ "failures."

B. ​Yes, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

C. ​No, because the sample is a simple random​ sample, the sample is less than​ 10% of the​ population, and there are at least 10 expected​ "successes" and 10 expected​ "failures."

D. ​No, because the sample is a simple random​ sample, the sample proportion is between​ 10% and​ 90%, and there are at least 20 expected​ "successes" and 20 expected​ "failures." ​

b) Construct a 95​% confidence interval for the proportion of​ "red snapper" packages that were a different kind of fish. (___________ , _____________) ​(Round to three decimal places as​ needed.) ​

c) Explain what the confidence interval from part​ (b) says about​ "red snapper" sold in these three states. Select the correct choice below and fill in the answer boxes within your choice. ​(Round to one decimal place as​ needed.)

A) One is 95% confident that between ________% and ______________% of all red snapper sold in food stores and restaurants in these states is not actually re snapper.

B) 98% of the time, the true proportion of red snapper sold in these three states is falsely labeled is between__________% and ________%.

C) One is 95% confident that between ______% and ________% of all red snapper purchased for the study in these states was not actually red snapper.

D) No, because the sample is a simple random sample, the sample proportion is between 10% and 90% and there are at least 20 expected "successes" and 20 expected "failures".

A researcher was curious about whether people’s attitudes are related to their behaviors. As a simple experiment, the researcher measured people’s attitudes and behaviors regarding housework.

On the attitude side, the researcher measured the level of agreement on the statement “It is much better for everyone involved in housework: strongly agree, agree, disagree, and strongly disagree” On the behavioral side, the respondents are asked to estimate how many hours of housework they do per week.

Based on your analysis of the data below, please come up with a conclusion whether people who respond differently to the attitudinal question actually behave differently?

Once you have arrived at an answer to each question, please write a sentence or two interpreting the result (100 pts).

1. State the null and alternative hypotheses. (15 pts)
2. Find the critical value from the F test distribution. (15 pts)
3. ANOVA computation (Mean and Variance of each sample groups were provided with the data.

c.1. Find the grand mean, the mean of all values in the samples. (10 pts)

c.2. Find the between-group variance. (15 pts)

c3. Find the within group variance.

c.4. Compute the F-value. (15 pts)

4. At α = 0.05, can it be concluded that there is a significant difference in the behavior among the groups with different attitudes toward housework? Why or why not? Make the decision and summarize the results. (15 pts)

12. The data below shows the annual salaries​ (in millions) and the number of viewers​ (in millions) of eight television actors and actresses. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using a=0.05. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Salary_(x)            Viewers_(y)

91           17

13           4.7

15           5.3

30           1.5

10           10.6

5              9.8

7              13.2

4              4.6

Construct the scatterplot.

The linear correlation coefficient r is _____

(Round to three decimal places as​ needed.)

The test statistic t is _____

(Round to three decimal places as​ needed.)

The​ P-value is ______

(Round to three decimal places as​ needed.)

Because the​ P-value is (greater,less) than the significance level 0.05​, there (is not, is) sufficient evidence to support the claim that there is a linear correlation between selling price​ (in hundred​ thousands) and the list price​ (in hundred​ thousands) of homes sold for a significance level of a=0.05.

Suppose that in a large population of students, the mean amount of sleep the previous night was μ = 7.15 hours and the standard deviation was σ = 1.5 hours. Consider randomly selected samples of n = 240 students.

(a) What is the value of the mean of the sampling distribution of possible sample means?
Mean =  

(b) Calculate the standard deviation, s.d., of the sampling distribution of possible sample means. (Round your answer to three decimal places.)

s.d.(x)

=

(c) Use the Empirical Rule to find values that fill in the blanks at the end of the following sentence. (Round your answers to three decimal places.)

For 68% of all randomly selected samples of n = 240 students, the mean amount of sleep the previous night will be between  and  hours.

(d) Use the Empirical Rule to fill in the blanks at the end of the following sentence. (Round your answers to three decimal places.)

For 95% of all randomly selected samples of n = 240 students, the mean amount of sleep will be between  and  hours.

Genetic analysis has shown that three recessive genes d (dwarf), e (enlarged trunk) and f (fine leaf) are all found on chromosome #1 of apple. When a plant that was heterozygous for each of these markers was testcrossed, the following 1000 progenies were obtained:

wild type- 130 (+++)

fine leaf- 19 (++f)

enlarged trunk- 2 (+e+)

enlarged trunk, fine leaf – 350 (+ef)

dwarf -362 (d++)

dwarf, fine leaf -1 (d+f)

dwarf, enlarged trunk -16 (de+)

dwarf, enlarged trunk, fine leaf- 120 (def)

a) Determine the central gene.

b) Calculate recombination frequencies between each of these three pairs of genes.

c) Draw a genetic map for the location of these 3 genes on chromosome #1 of apple. Show the map distances (cM or m.u.) between each loci.

d) Determine the interference among crossover events within the region of the chromosome containing the three genes.

Managers are required to make many tough decisions over the course of a work day. One of the tough decisions a manager may be faced with is the decision to drop an existing customer from their portfolio.

Some companies refuse to drop customers (including non-profitable customers) in the hopes that these unprofitable customers will become profitable in the future.

Other companies do not want unprofitable customers impacting their bottom line year after year and choose to drop them.

In your opinion, when should unprofitable customers be dropped (if at all)? Provide personal examples or research to help support your arguments.

The average number of customers visiting the science center was 800 per day last year and the populations standard deviation is 250 customers per day.

1. In a span of a month, i.e. 30 days, write out the distribution of the sample mean

2. What is the probability that the sample mean is over 275 customers per day in a month?

3. What is the probability that the sample mean is less than 275 customers per day in a month?

4. A good month means the average number of customers is more than the average of 95% of the other month. Determine the criteria of a good month.

Assume a standard customer, Johnny Rose, at a shop will spend 20 mins in the shop. The shop has 4 customers on average and service time is random with known distribution. The shop has 4 customers on average and service time is random with known distribution. How many customers does the shop serve during a typical open hour?

Now let's say the shop would like to decrease the average number of customers at any point, but assume it cannot control/influence arrival patterns of customers or service rate. How can this be achieved? Support with calculations and clear principles.

Hank would like to know how many customers are entering his propane store within a given timeframe.  Prior data indicate that on average 8 customers arrive in a given hour.

a. Create the appropriate probability distribution below for 0-12 arrivals.

b. What is the probability that 8 or fewer customers will arrive in the next hour?

c. What is the probability that exactly 10 customers arrive in the next hour?

d. What is the probability that more than 12 customers will arrive in the next hour?

e. How likely is it that Hank has a "large crowd" entering his store in the next hour?