5. A Pearson correlation statistic is only valid when the relationship between the two quantitative (continuous) variables is ____________.

1. Explain why it is true that the slope of a line is related to the Pearson correlation statistic, r.
   
2. Create a scatterplot to investigate the association between the amount of fluoride in domestic water (ppm) and the number of dental caries in permanent teeth per 100 children for 21 cities. The data are below.
   1. Create the scatterplot
   2. Describe the association you see in your scatterplot.
   3. The value of r is -0.86, -0.36, 0.36, or 0.86?

3. CityID	FLUORIDE (ppm)	CARIES
   1	1.9	236
   2	2.6	246
   3	1.8	252
   4	1.2	258
   5	1.2	281
   6	1.2	303
   7	1.3	323
   8	0.9	343
   9	0.6	412
   10	0.5	444
   11	0.4	556
   12	0.3	652
   13	0.0	673
   14	0.2	703
   15	0.1	706
   16	0.0	722
   17	0.2	733
   18	0.1	772
   19	0.0	810
   20	0.1	823
   21	0.1	1037

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.

Run the single-factor ANOVA for this data:

Fill in the summary table for the ANOVA test:

From this table, obtain the necessary statistics for the ANOVA:
F-ratio:  
p-value:  
η2=η2=

What is your final conclusion? Use a significance level of α=0.02α=0.02.

• These data do not provide evidence of a difference between the treatments
• There is a significant difference between treatments

1. Dinosaur fossils are too old to be reliably dated using carbon-14, which has a half-life of about 5730 years. Suppose we had a 68 million year old dinosaur fossil. How much of the living dinosaur's ¹⁴C would be remaining today? (Round your answer to five decimal places.)
______ %

Suppose the minimum detectable amount is 0.3%. What is the maximum age of a fossil that we could date using ¹⁴C? (Round your answer to the nearest integer.)
______ yr

2. A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (Round your answers to the nearest whole number.)

(a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 60 minutes?
T(60) = ____ °F

(b) When will the turkey have cooled to 100°?
t = _____ min

3. Use the Laws of Logarithms to combine the expression.

ln(10) + 3 ln(x) + 3 ln(x² + 10)

________

2. Suppose that the production function is Y=20K^0.3N^0.7. With the production function, the marginal product of labor is MPN=14K^0.3N^-0.3. The capital stock is K=214. The labor supply curve is NS=100[(1-t)w]², where w is the real wage rate, t is the tax rate on labor income, and hence (1-t)w is the after-tax real wage rate.

a)Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers.

b)Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6.

c)Suppose that a minimum wage $2 over the equilibrium wage is imposed. If the tax rate of labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?

Part c is needed.

One of the scenarios below is a Binomial Experiment and the other is not. For each​ scenario, state whether or not it is a Binomial Experiment. If it​ is, give the values of n and p and state all the possible values of X. If it is​ not, say why​ (which of the four conditions are not​ met?).

​(a) In the 2008 presidential​ election, 54% of the voters voted for President Obama. Suppose 5 people who voted in the 2008 election are randomly selcted. The random variable represents the number of people in the random sample who voted for President Obama in the 2008 election.

​(b) Suppose that the probability that a randomly selected person who has recently married for the first time will be divorced within 5 years is​ 0.2, and that the probability that a randomly selected person who has recently married for the second time is 0.3. We take a random sample of 20 people who recently married​ (10 for the first time and 10 for the​ second). The sample is chosen so that no one in the sample is married to anyone else in the sample. The

random variable represents the number of people in the sample of 20 who will be divorced within 5 years.

Question 2

Graph P(X=x) for binomial distributions with the following parameters
a) ? = 4 ??? ? = 0.5
b) ? = 4 ??? ? = 0.3
c) ? = 4 ??? ? = 0.1
d) Which if any of the graphs in part a-c are symmetric?
e) Without actually constructing the graph, would the case
? = 10 ??? ? = 0.5 be symmetric or skewed?
f) Which of the graphs in part a-c is the most heavily skewed?
g) Without actually constructing the graph, would the case ? = 4 and
? = 0.01 exhibit more or less skewness than the graph in part(c)?

Question 3

Suppose that a random variable y has a Poisson distribution.
Compute the following probabilities
a) P(y = 4) given ? = 3
b) P(y<4) given ? = 3
c) P(y<=4) given ? = 3
d) P(y>4) given ? = 3
e) P(2<y<5) given ? = 3

Question 4

The number of calls coming to the customer care center of a mobile company per
minute is a Poisson random variable with mean 5. Find the probability that no call
comes in a certain minute

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $5.2 million with a 0.2 probability, $1.5 million with a 0.5 probability, and $0.4 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.

Please show all work

You have a rubber ball having a radius of 0.5 m, a rubber cylinder have a height of 0.2 m and a radius of 0.3 m, and rubber cube have a side length of 0.2m. Assume they have very little mass, so their weight can be ignored. You have 3 m by 2 m by 1 m treasure chest that has a mass of 10000 kg.

Part a) How many spheres do you need to attach to the chest for it to float to the surface? Assume your spheres are massless and are completely submerged.

Part b) How many cylinders do you need to attach to the chest for it to float to the surface? Assume your cylinders are massless and are completely submerged.

Part c) How many cubes do you need to attach to the chest for it to float to the surface? Assume your cubes are massless and are completely submerged.

Part d) What is the waterline of the chest if you attach 10 spheres, 100 cylinders, and 800 cubes to the chest? Assume your spheres, cylinders, and cubes are massless and are completely submerged

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.7 million with a 0.2 probability, $1.7 million with a 0.5 probability, and $0.6 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

RÔE = % σ = % CV =

Debt/Capital ratio is 10%, interest rate is 9%.

RÔE = % σ = % CV =

Debt/Capital ratio is 50%, interest rate is 11%.

RÔE = % σ = % CV =

Debt/Capital ratio is 60%, interest rate is 14%.

RÔE = % σ = % CV =