7) Personal phone calls received in the last three days by a new employee were 4, 1, and 8. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a) List the nine different possible samples of size 2 and find the mean of each of them. b) The probability for each sample mean in Part a) is 1/9. Summarize your results in Part a) by construct ing a sampling distribution for these sample means. c) Find the expected value based on Part b). This expected value is also the mean of all the nine sample means found in Part a). d) Find the population mean of the personal phone calls received in the last three days by a new employee: {2, 3, 7} and compare it with your result in Part c).

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females.

x (lb) 23 27 22 26 20 15 25 21 17 24 26 22 18 19

y (lb) 127 124 117 125 130 120 145 130 130 130 130 140 110 115

In this setting we have Σx = 305, Σy = 1773, Σx2 = 6819, Σy2 = 225,669, and Σxy = 38,803. (

a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to four decimal places.) x = y = b = ŷ = + x

(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties.

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %

(d) Test the claim that the population correlation coefficient ρ is positive at the 1% level of significance. (Round your test statistic to three decimal places and your P-value to four decimal places.) t = P-value = Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0. Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0.

(e) If a female baby weighs 15 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb

(f) Find Se. (Round your answer to two decimal places.) Se =

(g) Find a 99% confidence interval for weight at age 30 of a female who weighed 15 pounds at 1 year of age. (Round your answers to two decimal places.) lower limit lb upper limit lb

(h) Test the claim that the slope β of the population least-squares line is positive at the 1% level of significance. (Round your test statistic to three decimal places and your P-value to four decimal places.) t = P-value = Conclusion Reject the null hypothesis. There is sufficient evidence that β > 0. Reject the null hypothesis. There is insufficient evidence that β > 0. Fail to reject the null hypothesis. There is sufficient evidence that β > 0. Fail to reject the null hypothesis. There is insufficient evidence that β > 0.

(i) Find a 99% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval. For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls within the confidence interval. For each pound less a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval. For each pound more a female infant weighs at 1 year, the adult weight increases by an amount that falls outside the confidence interval.

The physician wanted to know if conception periods were different due to the degrees of coffee drinking habit. Thus she collected data on the number of month to conception for 3 light coffee drinkers (1-2 cups per day), 4 moderate coffee drinkers (3-4 cups per day), and 3 heavy coffee drinkers (more than 4 cups per day). The table below summarizes the month to conception as a function of the three groups (light, moderate, and heavy coffee drinkers).

You are asked to analyze the above data with one-way ANOVA. Please answer the following questions with regards to one-way ANOVA on the above data.

1. State the null and alternative hypotheses (2pts)

2. Identify the degrees of freedom(s). (2pts)

3. Identify the F critical based on the degrees of freedoms above by consulting with F table (2pts)

4. Here is the summary table presenting SSwithin, SS between, and SStotal. Please compute F value based on SSs and Degrees of Freedoms that you identified in the above. This should require computing MSwithin, MSbetween, and F. (2pts each for these three values)

I have these answers to 1-4

1. The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

2. df = 9

3. F critical = 4.74

4.

5. State your decision on the hypothesis based on the calculation above that led to the F value (2pt).

6. You tried to replicate above study with the exact same number of participants, and you got the following results:

You may notice that the means of the three groups are the same as the previous results with three means for L, M, H conditions being 5, 6, and 9 respectively. Please fill out the blank sections of the summary table below based on your understanding/knowledge of how One-way ANOVA works. If you get the correct F value, you will get 9pts. If you do not get the correct F value, 1 pt is given for each of the 6 values (SSs, DFs, and MSs) that is correct.

7. Please compare the two results (and two summary tables), and explain why this difference in F values occurred across the two studies. The explanation should involve the concept of variance between and variance within. (3pt)

a) In the first trading day of 1998, Hang Seng Index closed at 10680.60, while in the last trading day of 2017, it closed at 29919.15. What is the average annual growth rate of Hang Seng Index in this 20-year?                              

b) The following yield curve is observed of the U.S. Treasury securities on 28th October 2019:

Suppose the pure expectation theory is correct. Forecast the expected one-year yield rate of one year later and of two years later respectively.  

Review Handout | Absolute Advantage and Comparative Advantage | Cases 1-3 (3 pages)

*Holding other things constant and considering the usual assumptions for the 2C-2G-1F model and production per unit of labor for both Case 1 and Case 2 below, determine which country has the absolute advantage and comparative advantage in which good.

Example Case 1

To determine who has a comparative advantage in which good, we will need to calculate opportunity costs of good X and good Y in each country first.

In the case of Country A above, the opp. cost of X (in terms of Y) is the number of units of Good Y Country A should give up in order to produce one more unit of Good X.   To find out this, we can simply divide the number of Good X and Good Y per unit of labor in each cell by 60, respectively, so that we can see how many units of Good Y Country A should give up to produce one more unit of Good X in Country A.   As shown above, it will be 1.33.  

By the same token, in the case of Country A, the opp. cost of Y (in terms of X) is the number of units of Good X Country A should give up in order to produce one more unit of Good Y.   To find out this, we can simply divide the number of Good Y and Good X per unit of labor in each cell by 80, respectively, so that we can see how many units of Good X Country A should give up to produce one more unit of Good Y in Country A.   As shown above, it will be 0.75.  

1. Which country has an absolute advantage in producing X and Y, respectively?

Hint) Per unit of labor, which country is producing Good X (Good Y) more in absolute terms?

2. Country A has a comparative advantage in producing:

3. Country B has a comparative advantage in producing:

Case 2

1. Which country has an absolute advantage in producing wine and wool, respectively?

2. Portugal has a comparative advantage in producing:

3. The U.K. has a comparative advantage in producing:

Case 3. Now assume that country “American” can produce either 20 songs or 40 boxes of roses per week. Assume that country “Eagle” can produce 10 songs or 50 boxes of roses per week. Consider the usual assumptions holding other things constant.

1. Which has a comparative advantage in the production of songs?

2. Which has a comparative advantage in the production of roses?

3. If each produces songs for one week and then roses for one week, show the total    production of both goods.

4. Now, assume each country specializes for two weeks. Indicate the total production of both goods. Show that trade between the two countries after this two-week period can allow both countries to consume both more roses and songs.

1. Assume there are 5 seats to vote in the board of directors. There are only three shareholders: Arnold (100 shares), Beth (40 shares), and Charles (60 shares). With cumulative voting Charles can elect at least _________.

Select one:

a. zero directors

b. one director

c. two directors    

d. three directors   

2If a savings account pays an annual interest of 2% compounded quarterly, then the quarterly interest rate should be less than 0.5%.

Select one:

True

False

3.If a company is liquidated, preferred shareholders have a first claim on the company assets than subordinate debt holders.

Select one:

True

False

4Assume you invest $20,000 with expected cash flows of $10,500 and $11,025 in periods one and two respectively. If the discount rate is 5% then the net present value of your investment is $1,525.

Select one:

True

False

5.An example of indirect finance is when companies issue bonds instead of getting loans from commercial banks.

Select one:

True

False

A airline wishes to estimate the mean number of seats that are empty on flights that use 737-airplanes. There are 189 seats on a plane. To do so, the airline randomly picks n=35 flights. For each flight, the number of empty seats is counted. The data are given below.

38, 42, 44, 42, 40, 45, 37, 31, 33, 36, 35, 39, 37, 37, 43, 38, 41, 27, 33, 35, 37, 46, 32, 35, 35, 42, 37, 41, 29, 40, 44, 34, 34, 41, 29

(a) Find the mean and the standard deviation of this sample. Use at least three decimal places in each answer.

(b) To construct a confidence interval for the mean number using the T distribution for unoccupied seats on all flights, what condition must you hold?

A. That the number of unoccupied seats are normally distributed.

B. The sample size is sufficiently large for the Central Limit Theorem to provide a valid approximation.

C. The number of unoccupied seats can be modeled by the Binomial distribution.

D. The number of unoccupied seats are not normally distributed.

(c) Find a 90% Student T confidence interval for μ, the mean number of empty seats on this airline's flights. Use at least three decimal points for your lower and upper bounds.

Lower Bound =

Upper Bound

(d) Find a 90% confidence interval for μ, the mean number of empty seats on this airline's flights, by Bootstrapping 1000 samples. Use the seed 7775 to ensure that R-Studio "randomly" samples the same "random" samples as this question will expect.

You can do this by including the code, you can copy it into your R-Studio to bootstrap your samples.

RNGkind(sample.kind="Rejection");

set.seed(7775);

B=do(1000) * mean(resample(c(38, 42, 44, 42, 40, 45, 37, 31, 33, 36, 35, 39, 37, 37, 43, 38, 41, 27, 33, 35, 37, 46, 32, 35, 35, 42, 37, 41, 29, 40, 44, 34, 34, 41, 29), 35));

Use at least three decimal points for your lower and upper bounds.

Lower Bound =

Upper Bound =

If we recreated the scene from Fast & Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft at 5,280 ft, how much horsepower would it take to drive past it before it hits the ground if you’re 1 mile away?