A company recently switched its compensation plan. Prior to the switch, salespeople were paid a higher salary, but their commission on each item sold was smaller. After the switch, the salary was less, but the commission for each item sold was larger. A complaint was lodged with HR with the threat of legal action claiming the sales team was making less money. The HR director examined the salaries of nine randomly selected salespeople. Their salaries ($1000’s) before and after the switch are shown in the table below.

Salesperson 1 2 3 4 5 6 7 8 9

Before 55 22 34 22 25 61 55 36 68

After 53 24 36 28 31 61 58 38 72

(a) Is there evidence that salaries decreased under the new compensation plan? Test at the 2.5% level of significance.

(b) Explain the meaning of the P-value in the context of the study.

(c) Explain the meaning of a Type I error in the context of the study.

(d) Explain the meaning of a Type II error in the context of the study.

Grocery workers are one of the essential workers in the time of COVID19 pandemic. One of the grocery workers are Costco workers. Suppose that the Costco company wants to hire more workers due to COVID 19 and Costco workers want to work fewer hours due to COVID 19. What will happen to equilibrium wage per hour of Costco workers and equilibrium number of hours of Costco workers? Analyze how equilibrium wage and number of working hours will change due to COVID 19 in three graphs because there may be three cases depending on the relative size of change in labor demand and labor supply. Label clearly Y-axis, X-axis, and two equilibrium points as E₀ before COVID 19 and as E₁ after COVID 19 and labor demand and supply as LD₀ and LS₀ before COVID 19 and labor demand and supply as LD₁ and LS₁ after COVID19. Show the change in equilibrium wage and working hours by arrows and summarize how these two (wage and working hours) changes in each case in words after drawing graphs.

In a certain scattering experiment, protons with mass m are fired with initial kinetic energy K0 (momentum p0) at a target consisting of helium atoms (the mass of a helium atom is approximately 4m). Protons scattered at an angle of 90◦ relative to their initial direction of motion are measured to have a kinetic energy of Kp = 0.54K0 (corresponding to a momentum of pp). Assuming that each outgoing proton collided with one and only one helium atom, is this collision elastic, or has the helium atom increased its internal energy during the collision (it is very hard to increase the internal energy of a proton)? Follow the steps outlined below in order to answer this question. a. (2 points) Draw a useful before and after picture and label it with appropriate symbols. b. (2 points) Find the momentum of the proton, pp, after the collision relative to the momentum of the proton, p0, before the collision. c. (3 points) Use a conservation law to determine the components of the helium atom’s momentum, ~pH, after the collision in terms of p0. d. (3 points) Use a conservation law and correct algebra to answer the question posed.

A 1700 kg car moving east at 17 m/s collides with a 1800 kg car moving south at 20 m/s, and the two cars stick together. Consider east the positive x-direction and north the positive y-direction.

a) What is the x-component of the initial momentum before the collision? ( -7100 kg·m/s, 64900 kg·m/s or 28900 kg·m/s)

b) What is the y-component of the initial momentum before the collision? (-36000 kg·m/s, -7100 kg·m/s, 64900 kg·m/s or 36000 kg·m/s)

c) What is the x-component of the two cars’ final velocity after the collision? (8.26 m/s, 17 m/s, 16.06 m/s)

d) What is the y-component of the two cars’ final velocity after the collision? (-20 m/s, -21.18 m/s, -10.29 m/s or 10.29 m/s)

e) What is the speed of the two cars after the collision?

f) How much kinetic energy is lost in the collision?

4. Southwire believes that they will obtain seven new medium-sized clients per quarter. From 24 quarters of past accounts receivable history, you find that they have obtained an average of 8.4 clients, with standard deviation of 2.5.
(a) What is the appropriate null and alternative hypothesis?

(b) Write down the appropriate test-statistic.

c) Compare your test-statistic to appropriate critical values. Do you reject the null, and at what levels?

(d) Now suppose that Southwire believes that, after running a marketing campaign, the number of large-sized clients added per quarter will increase from prior to the campaign. They do a comparison of the 12 months before the campaign to the 12 months after. Before, an average of 2.3 large-sized clients were added. After, 3.1 were added. The standard deviation of the differences is 1.5. i. Write down an appropriate null and alternative hypothesis. ii. What is the appropriate test statistic? iii. Test your hypothesis at all appropriate levels. Do you reject the null, and at what levels

Describe elastic, inelastic, and completely inelastic collisions. Which type of collisions are you going to investigate in the lab?

Do you expect the linear momentum of the system to be conserved in your experiment?In which part? Explain why.

Do you expect kinetic energy of the system to be conserved in your experiment? In which part? Explain why.

In one trial for inelastic collisions in the experiment, cart 1 has mass m1 and is initially moving with velocity v ⃗_1i to the right. Cart 2 with mass m2 is initially moving with velocity v ⃗_2i also to the right. The velocity of the cart 1 is larger than the velocity of cart 2 causing a collision between both carts. After the collision, the carts stick together and move with velocity v ⃗_f to the right.

Write down the expression for the magnitude of linear momentum of the system before collision.

Write down the expression for the magnitude of linear momentum of the system after the collision.

Write down the expression for the magnitude of kinetic energy of the system before collision.

Write down the expression for the magnitude of the kinetic energy of the system after the collision.

4. To determine the effectiveness of a proposed public relations campaign, the senior vice president for customer relations for an automobile manufacturer asked seven consumers how much they liked the company (on a scale from 0 [do not like] to 50 [like very much]) before and after viewing the primary television advertisement of the campaign. Use the following data to test whether the consumers’ ratings of the company increased, on average, after viewing the television advertisement:

a. State the null and alternative hypotheses associated with the test.
b. If α = 0.05, what is the critical value of the associated test statistic?
c. What is the calculated value of the associated test statistic?
d. State your decision about the null hypothesis by comparing the critical and calculated values of the test statistic (Parts b and c).
e. Comment on the effectiveness of the primary television advertisement of the campaign.

When a patient has a suspected vestibular disorder, the physician orders an electronystagmography (ENG) test. Which instructions should the nurse include when educating the patient about this test? Select all that apply. The patient my have caffeine or alcohol up to 3 hours before the test. The patient does not need to bring normally worn eyeglasses to the test. The patient may experience nausea after the test. Electrodes will be placed around the eyes. The patient should have nothing to eat or drink 3 hours before the test.

A mass; m1 = 64 g, sits on a frictionless horizontal surface, and is attached to a spring of spring constant k = 51 N/m. The other end of the horizontal spring is attached to a wall; the system is in equilibrium. Another mass; m2 = 18 g, strikes the stationary mass m1, and sticks to it. As a result, the spring is compressed by a distance of 24.5 cm before the masses come to a momentary stop.

a) How fast was m2 moving before the collision?

b)How long does it take the masses to come to a momentary stop after the collision?

For each scenario listed on the left, determine whether the scenario represents an Indepenent Samples or Matched pairs situation by placing the appropriate letter in the box provided.

• -ab Comparing pain levels of a group receiving a placebo to a group receiving a medicine
• -ab Comparing pre-test scores before training to post-test scores
• -ab Comparing the number of speeding tickets received by men to the number received by women
• -ab Comparing pain levels before and after treatment with magnetic therapy

a. Independent Samples

b. Matched Pairs