An insurance company has three types of annuity products: indexed annuity, fixed annuity, and variable annuity. You are given:

• None of the customers have both fixed annuity and variable annuity.
• 40% of the customers with fixed annuity also have indexed annuity.
• Half of the customers with two annuity products have variable annuity.
• 60% of the customers have indexed annuity.
• The number of customers who have only the variable annuity is the same as the number of customers who have two annuity products.
• All customers have at least one type of annuity.

Determine the proportion of the customers who only have the indexed annuity.

1. 0.35

2. 0.37

3. 0.39

4. 0.41

5. 0.43

Your friend has chosen a card from a standard deck of 52 playing cards and no one knows the card except himself. Now you have to guess the unknown card. Before guessing the card, you can ask your friend exactly one question, the question must be either Q1, Q2 or Q3 below:

Q1. whether the chosen card is a king (K)?

Q2. whether the chosen card is a spade (♠)?

Q3. whether the chosen card is the king of spades (K♠)? Your friend will answer truthfully. What question would you prefer to ask so that it is more helpful to make a correct guess? Justify your answer.

Use the Beach Front Hotels data set to do the following. In each of the three problems below, we will test the null hypotheses that each of the means is equal to 90 against the alternative hypotheses that each of the means is unequal to 90. Fill in the numerical values to three decimal places. #1 99% confidence intervals (6 Points) Overall Comfort Amenities In-House Dining Lower 99% CI Upper 99% CI For overall, Maintain/Reject Ho at .01 because_____________ #2 t-statistics and the critical values (8 points Overall Comfort Amenities In-House Dining t-stat t-crit .05 ± ± ± ± t-crit .01 ± ± ± ± For Amenities, Maintain/Reject Ho at .01 because_____________ #3 Determine the four p-values (6 points) Overall Comfort Amenities In-House Dining p-values For Comfort, Maintain/Reject Ho at .01 because_______________ Data for Beach Front Hotels Overall Comfort Amenities In-House Dining 94.3 94.5 90.8 97.7 92.9 96.6 84.1 96.6 92.8 99.9 100.0 88.4 91.2 88.5 94.7 97.0 90.4 95.0 87.8 91.1 90.2 92.4 82.0 98.7 90.1 95.9 86.2 91.9 89.8 92.5 92.5 88.8 89.3 94.6 85.8 90.7 89.1 90.5 83.2 90.4 89.1 90.8 81.9 88.5 89.0 93.0 93.0 89.6 88.6 92.5 78.2 91.2 87.1 93.0 91.6 73.5 87.1 90.9 74.9 89.6 86.5 94.3 78.0 91.5 86.1 95.4 77.3 90.8 86.0 94.8 76.4 91.4 86.0 92.0 72.2 89.2 85.1 93.4 77.3 91.8

1. For the andorian species, if the probability that a couple produces a girl is 0.97193, and if the couple has 8 children, what is the probability they will have:
5 boys and 3 girls (in any order)?

2. For the Vulcan species, if the probability that a couple produces a girl is 0.23477, and if the couple has 5 children, what is the probability they will have:
3 boys and 2 girls (in any order)?

Question 1:

Which is best practice?

• A. Contrasts of interest are determined by research questions and should be explicitly stated at the planning stage of an experiment.
• B. Contrasts of interest are best determined during the exploratory data analysis stage.
• C. The contrasts one should investigate are determined by the observed difference between treatment means; bigger observed differences are more interesting

Question 2

Which of the following is a contrast and orthogonal to

?1=4?1−(?2+?3+?4+?5)

• A.

  ?2=?1−?3

• B.

  ?3=4?1+(?2+?3+?4+?5)

• C.

  ?4=?2−?3

Question 3

A contrast is a comparison of means.

Question 4:

Which of the following qualifies as a contrast?

• A.

  ?1=0.5?1+0.5?2

• B.

  ?2=??1–0.5(?2+?3)

• C.

  ?3=?1+?2+?3

• D.

  ?4=13(?1+?2+?3)

Show all details. Thanks

Consider 2 models:

where Equation (1) represents a system of n scalar equations for individuals i = 1; ...; n , and
Equation (2) is a matrix representation of the same system. The vector Y is n x 1. The matrix X0
is n x 2 with the first column made up entirely of ones and the second column is x1; x2; ...; xn.
a. Set up the least squares minimization problems for the scalar and matrix models.
b. Show that the β terms from each model are algebraically equivalent, i.e. the β1 and β2
you get from solving the least squares equations from Equation (1) and the matrix algebra
problem from Equation (2) are identical.

Discuss some of the possible" lurking variables" that may exist below.

Researchers observe that there is a correlation between the number of glasses of red wine a person drinks per week, and the number of illnesses the person has. They conclude that drinking red wine causes a person to be healthier.

A is called a palindrome if it reads the same from left and right. For instance, 13631 is a palindrome, while 435734 is not. A 6-digit number n is randomly chosen. Find the probability of the event that

(a) n is a palindrome.

(b) n is odd and a palindrome.

(c) n is even and a palindrome.

Sparrowhawk colonies. One of nature’s patterns connects the percent of adult birds in a

colony that return from the previous year and the number of new adults that join the colony. It

is expected that the percent return of adult birds from the previous year can be used to predict

how many new adult birds will join a colony. The data set sparrowhawk.xlsx contains

information for 13 colonies of sparrowhawks. The variables are the percent of adult birds in a

colony that return from the previous year (Percent return) and the number of new adults that

join the colony (New adults).

(a) Using an appropriate graphical display and the summary statistics, describe the distribution

of the percent of adult birds in a colony that return from the previous year (Percent return).

(b) Using an appropriate graphical format, display AND describe the relationship between the

percent of adult birds in a colony that return from the previous year (Percent return) and

the number of new adults that join the colony (New adults).

(c) Find the sample correlation coefficient between the percent of adult birds in a colony that

return from the previous year (Percent return) and the number of new adults that join the

colony (New adults). Comment.

(d) Fit a least-squares line to the data. Write down the equation of the fitted line (model) and

interpret all parameters in the model

(e) Predict how many new adult birds will join the colony, when 30% and 70% of the adults

from the previous year return respectively

Translate the following argument to symbolic notation (be sure to provide the dictionary) and then use a truth table to show that the argument is an invalid argument. State how the truth table shows that the argument is invalid.

If Elle is a member of Delta Nu, then she comes from a rich family. Elle’s family is rich. Therefore, Elle belongs to Delta Nu.

Let X ~ exp(λ)

MGF of X = λ/(1-t)

a) What is MGF of Y = 3X

b) Y has a common distribution, what is the pdf of Y?

c) Let X1,X2,....Xk be independent and identically distributed with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below the summation symbol, and k is on top of the summation symbol). What is the MGF of S?

d) S has a common distribution. What is the pdf of S?

5.29 Catalog Age lists the top 17 U.S. firms in annual catalog sales. Dell Computer is number one followed by IBM and W.W. Grainger. Of the 17 firms on the list, 8 are in some type of computer-related business. Suppose four firms are randomly selected. a. What is the probability that none of the firms is in some type of computer-related business? b. What is the probability that all four firms are in some type of computer-related business? c. What is the probability that exactly two are in non-computer-related business?

5.26 A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Consider a sample in which 300 people are randomly selected who have fractured or dislocated a bone. a. What is the probability that exactly five of them did not see a doctor? b. What is the probability that fewer than four of them did not see a doctor? c. What is the expected number of people who would not see a doctor?

a. Your boss asks you to conduct a hypothesis test about the mean dwell time of a new type of UAV. Before you arrived, an experiment was conducted on n = 5 UAVs (all of the new type) resulting in a sample mean dwell time of ybar = 10.4 hours. The goal is to conclusively demonstrate, if possible, that the data supports the manufacturerer's claim that the mean dwell time is greater than 10 hours. Given that is is reasonable to assume the dwell time are normally distributed, the sample standard deviation is s = .5 hours, and using a significance level of alpha = .01, conduct the appropriate hypothesis test.

b. For the hypothesis test constructed, what is the probability of a Type II error if the true mean is 10.4 hours? Interpret in your own words.

c. What is the probability of a Type II error if the true mean were actually 11 hours? What do your answers from b. and c. tell you about the power of your hypothesis test?