A shoe company wants to test if three groups of workers have different salaries.

Group (1): 23, 41, 54, 66, 78

Group (2): 45, 55, 60, 70, 72

Group (3): 18, 30, 34, 40, 44

Use kruskall Wallis test with α = 0.05.

Find Chi-Square value of Age out of 1,000 Americans

9.9. Is gender independent of education level? A random sample of people were surveyed and

each person was asked to report the highest education level they obtained. Perform a hypothesis

test. Include all 5 steps.

After graduating from UTD at age 25, John got his first job at Goldman Sachs with an annual salary of $60,000 a
year and a one-time signing bonus of $25,000. He bought a car using his signing bonus. Goldman Sachs offers a
401K retirement investment plan that will match employee’s contribution up to 10%. For example if John invests
1% in the 401K account, Goldman Sachs will put in another 1% into his account. John is expecting an annual
salary increase of 2.4% (APR on a monthly base. For simplicity, assume that the growth will start in the second
month). Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base).
(Assume the beginning of age 25 is month 0 and salary is paid at the end of each month, i.e., beginning of age 65 is
the last period)
(a) What percentage of salary should John invest in his 401K account in order for him to have $2 million in the
account when he retires in 40 years?
(b) At the same contribution rate, if he retires in 35 years instead, how many percent less money will John have?
(c) Instead of buying a nice car, he brought a used car for $10,000, and saved the rest of signing bonus in a separate
investment account for retirement that pays 9.6% annual interest (APR on a monthly base). If John wants to
have $2 million when he retires in 35 years, what percentage of salary should John invest in his 401K account?After graduating from UTD at age 25, John got his first job at Goldman Sachs with an annual salary of $60,000 a
year and a one-time signing bonus of $25,000. He bought a car using his signing bonus. Goldman Sachs offers a
401K retirement investment plan that will match employee’s contribution up to 10%. For example if John invests
1% in the 401K account, Goldman Sachs will put in another 1% into his account. John is expecting an annual
salary increase of 2.4% (APR on a monthly base. For simplicity, assume that the growth will start in the second
month). Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base).
(Assume the beginning of age 25 is month 0 and salary is paid at the end of each month, i.e., beginning of age 65 is
the last period)
(a) What percentage of salary should John invest in his 401K account in order for him to have $2 million in the
account when he retires in 40 years?
(b) At the same contribution rate, if he retires in 35 years instead, how many percent less money will John have?
(c) Instead of buying a nice car, he brought a used car for $10,000, and saved the rest of signing bonus in a separate
investment account for retirement that pays 9.6% annual interest (APR on a monthly base). If John wants to
have $2 million when he retires in 35 years, what percentage of salary should John invest in his 401K account?

The company you are working for has decided to put on a banquet to raise money for a charity and must decide between two catering services to supply the food and servers. You have been assigned to the Banquet Planning Committee. Simplify completely.

Research Provided

The company's research department has provided the following estimates.

• A demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each.

• Catering Service A has a fixed cost of $1,900 and a marginal cost of $30 for each plate.

• Catering Service B has a fixed cost of $3,000 and a marginal cost of $22 for each plate.

• Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup.

• Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing.

• Additional spontaneous donations to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500.

Analysis

Each team should perform the following analyses:

1. Assume the price-demand function is linear. Use the research estimates to find the relationship between the price p, and the number of banquet attendees demanded, x. Find the relevant domain.

2. Find the revenue function, R(x), in terms of the number of banquet attendees x. Find the relevant domain by considering realistic limitations on the number of attendees and on price. Sketch a graph on the work page.

3. Assume the cost function is linear and use the research estimates to find the cost function for each of the two possible catering services in terms of the number of banquet attendees x. Sketch a graph on the work page.

4. Determine the break-even quantities for each of the two possible catering services.

5. Find the Profit function, P(x), for each of the two possible catering services in terms of the number of banquet attendees x.

6. If it is projected that there will be 100 tickets sold at a dinner price of $112.50, which catering service should the committee recommend in order to earn the most profit for the charity?

7. Decide which catering service your company should choose if the projections yield 200 attendees. Include the ticket price at this demand.

8. Find the average cost function for Catering Service A. Evaluate the average cost per attendee if 50 tickets are purchased. Evaluate the average cost per attendee if 400 tickets are purchased.

9. On average, how much can you expect to receive in spontaneous donations for each banquet attendee? (Determine the per person expected value (weighted average) of donations.) Which charity does the committee recommend for receipt of banquet donations?

10. Overall recommendations: Which catering service does your committee recommend in order to obtain the most profit for the charity? How many people should attend the banquet to earn that profit and what profit can be expected from the banquet ticket sales? What price would you recommend for each dinner plate (ticket)? What dollar amount is expected from spontaneous donations? What will be the expected total amount raised for the charity (including the dinner ticket profits and spontaneous donations)?

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 30%of the time on airline #3. For airline #1, flights are late into D.C. 15% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 40% and 30%, whereas for airline #3 the percentages are 35% and 20%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.)

A girl of mass, m = 40 kg has osteoporosis which weakens her bones. From a kneeling position, she topples forward onto her elbows with her upper arms extended vertically downwards on impact with the ground. In falling forward, her centre of mass lowers by a height, h = 50 cm and she absorbs all of her kinetic energy from her fall into her two humerus bones (one bone in each upper arm).

Determine an equation for the stress in each humerus bone, ?, in terms of m, h, the acceleration due to gravity, g, Young’s modulus for bone, Y, the cross sectional area of each humerus bone, A and the length of each humerus bone, l. State any laws used. Now, determine the minimum rupture strength required for the girl’s humerus bones such that she doesn’t break them, given in units of N/m2 . Take l = 20 cm, A = 3.0 cm2 and Y = 1.4 x10^10 N/m2 .

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

(a) Find Σx, Σy, Σx², Σy², Σxy, and r. (Round r to three decimal places.)

(b) Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.)

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 insufficient evidence that ρ > 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0.

(c) Find S_e, a, b, and x. (Round your answers to four decimal places.)

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 80% successful free throws. (Round your answer to two decimal places.)
%

(e) Find a 90% confidence interval for y when x = 80. (Round your answers to one decimal place.)

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

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 insufficient evidence that β > 0.Fail to reject the null hypothesis, there is sufficient evidence that β > 0.

TRUE/FALSE.

1. In a repressible operon transcription is normally turned off.

2) A Monoybrid cross involves one gene and two or more different alleles.

3) Crossing over during meiosis occurs in the Metaphase II stage.

4) In prokaryotes, transcription and translation are separated in time and space.

5) Crossing over takes place in meiosis and is responsible for recombination.

6) Natural selection can lead to a decrease in genetic variation both within and between populations.

7) The pyrimidine bases in nucleic acids are adenine and guanine.

8) The poly(A) tails on mRNA molecules are transcribed from DNA templates.

9) Exons are degraded in the nucleus. 10) Most DNA binding motifs, such as leucine zippers, and Zinc fingers, have the binding the major groove of DNA. site in