An experiment was conducted to test the effect of a new drug on a viral infection. After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection, and the second group received the drug. After a 30-day period, the proportions of survivors, p̂₁ and p̂₂, in the two groups were found to be 0.38 and 0.62, respectively.

(a) Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

(b) Use a 95% confidence interval to estimate the actual difference (p₁ − p₂) in the survival rates for the treated versus the control groups. (Round your answers to two decimal places.)

The data below are the healing rates of cuts (micrometers per hour) in a matched pairs experiment. The pairs are the two hind limbs of the same newt. In each pair, one limb had reduced electrical field and the other (the control) had its natural electrical field.

Is there good evidence that changing the electrical field from its natural level slows healing? Assume that all conditions for inference are met. Perform a hypothesis test. The p-value for your test is

Use the data in the following table to create a fraction nonconforming (p) chart. The column of np represents the number of non-conforming units. Is the process in control? (5 points)

Question 2

A bank's manager has videotaped 20 different teller transactions to observe the number of mistakes being made. Ten transactions had no mistakes, five had one mistake and five had two mistakes. Compute proper control limits at the 90% confidence level. Is the process in control? Show your work.

2. Find the following probabilities.
(a) Suppose 75% of women live past age 65 and 55% of women live past age
80. What is the probability that a woman who is now 65 will live past 80?
(b) What’s the probability that a roll of two fair six-sided dice will sum to 6?
What’s the probability of this once you observe that one of the dice came
up 2?
(c) A fair six-sided dice is tossed twice. The second toss is higher than the
first. What’s the probability that the first toss was at least 4?

4. Recall the cookie problem from lecture. We have two bowls, Bowl 1 and Bowl 2. Bowl 1 contains 25%
chocolate and 75% vanilla cookies; Bowl 2 has 50% of each. For this problem, assume each bowl is large
enough that drawing a single cookie does not appreciably alter this ratio.
Suppose we draw two cookies from the bowl and they are both chocolate. Calculate the posterior
probabilities of the two bowls in two ways:
(a) by treating the two cookies as one simultaneous piece of evidence
(b) by updating the prior probabilities once using the rst chocolate cookie, and using the posterior
probabilities as prior probabilities in a second update.

5. Suppose instead we draw two cookies; one is chocolate and the other is vanilla. Calculate the posterior
probabilities. Does it matter which cookie we drew rst? Why or why not?

Two Hollywood companies had the following balance sheet accounts as of December 31, 20X7 ($ in millions):

                                         Lexia   Hudson                                        Lexia       Hudson
Cash and receivables       $60   $44        Current liabilities               $100       $40
Inventories                         240   6            Common stock                   200       20
Plant assets, net                300   190        Retained earnings              300       180
Total assets                      $600   $240     Total liab. and stk. eq.       $600       $240
Net income for 20X7         $38     $8

On January 4, 20X8, these entities combined. Lexia issued $360 million of its shares (at market value) in exchange for all the shares of Hudson, a motion picture division of a large company. The inventory of films acquired through the combination had been fully amortized on Hudson's books.

During 20X8, Hudson received revenue of $42 million from the rental of films from its inventory.
Lexia earned $40 million on its other operations (i.e., excluding Hudson) during 20X8. Hudson
broke even on its other operations (i.e., excluding the film rental contracts)
during 20X8.

1. Prepare a consolidated balance sheet for the combined company immediately after the combination. Assume $160 million of the purchase price was assigned to the inventory of films. The fair values of all other Hudson assets and liabilities were equal to their book values.

2. Prepare a comparison of Lexia's consolidated net income between 20X7 and 20X8, where the cost of the film inventories would be amortized on a straight-line basis over 4 years. What would be the net income for 20X8 if the $160 million were assigned to goodwill instead of the inventory of films and goodwill was not amortized?

A heavy equipment manufacturer procures an Anti-lock Braking System (ABS) from two suppliers, Movis and Telphi, to reduce the risk of supply chain disruption. Movis supplied 100 ABSs last month, while Telphi did 150 ABSs last month. The manufacturer selected ten ABS samples and conducted an inspection.

(a) What is the probability that no ABSs from Movis is selected in the ten ABS samples?

(b) What is the probability that at least one ABSs from Movis are selected in the ten ABS samples?

(c) Assuming that both suppliers have the same defective rate of 0.01, what is the Probability that there is only one defective out of the 10 ABS samples?

5. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.

b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.

c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.

d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.

5. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.

b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.

c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.

d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ

. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.
b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.
c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.
d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.

Attached is a spreadsheet showing the most recent financial statements for Wall Enterprises. Please do your calculations on the spreadsheet. Using the percent of sales method forecast the financial statements for the next three years. Sales are anticipated to grow by 10%, 8%, and 5% thereafter. The WACC is 9%. Balance the balance sheets by using the Line of Credit or adding a Marketable Securities line if needed. The interest rate on all debt is 8% and is based on the debt outstanding at the end of the prior year. Dividends are forecast to grow by 10% each year. No additional long-term debt or commons stock will be sold. Make a note of anything you assumed in your forecast. Calculate the FCF and the terminal value to determine the value of the company. Given the 10 million shares outstanding what is the implied stock price? If an investor is willing to pay $250 million for 25% of the company, assuming a terminal value of 8X EBIT in 2019, (ignore the DCF calculations you just did) what return on investment does that provide? Is that likely to be an acceptable investment to the investor?