A stress researcher is measuring how fast parents respond to a crying infant. He gathers data from 64 people (N = 64). His participants' reaction times are normally distributed. The average reaction time was 3.0 seconds, with a standard deviation of 0.2 seconds. Using a standard normal table (Table A-1), answer the following questions (hint: you need to convert raw scores into z-scores).

a. What proportion of his participants will be between 2.6 and 3.1 seconds?
b.      What proportion of his participants will be between 2.4 and 3.2?
c. What proportion of his participants will be between 3.3 and 3.7?
d. What proportions of participants will be above 3.4 seconds?
e. Of the z-scores you calculated above which is the most probable? Which is the least probable? Explain your answers.
f. What would the standard error of the mean be for the sampling distribution from which this sample of reaction times was drawn, if we assume the population SD (sigma, σ) is also 0.2?
g. If we are using an alpha = .05, what would the critical values be in raw units (hint: you don't need the z-table for this)?

An economist wondered if people who go grocery shopping on weekdays go more or less often on Fridays than any other day. She figured that if it were truly random, 20% of these shoppers would go grocery shopping on Fridays. She randomly sampled 75 consumers who go grocery shopping on weekdays and asked them on which day they shop most frequently. Of those sampled, 24 indicated that they shop on Fridays more often than other days.

The economist conducts a one-proportion hypothesis test at the 1% significance level, to test whether the true proportion of weekday grocery shoppers who go most frequently on Fridays is different from 20%.

(a) H0:p=0.2; Ha:p≠0.2, which is a two-tailed test.

(b) Use Excel to test whether the true proportion of weekday grocery shoppers who go most frequently on Fridays is different from 20%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

Provide your answer below:

test statistic =    p-value =

A paddle ball toy consists of a flat wooden paddle and a small rubber ball that are attached to each other by an elastic band (figure). You have a paddle ball toy for which the mass of the ball is 0.014 kg, the stiffness of the elastic band is 0.890 N/m, and the relaxed length of the elastic band is 0.325 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is <−0.02, −0.01, −0.02 > kg·m/s, and the moving ball is at location <−0.2, −0.61, 0> m relative to an origin located at the point where the elastic band is attached to the paddle.

(a) Determine the position of the ball 0.1 s later, using a Δ⁢t of 0.1 s. (Express your answer in vector form.)

(b) Starting with the same initial position (<−0.2, −0.61, 0> m) and momentum (<−0.02, −0.01, −0.02 > kg·m/s) determine the position of the ball 0.1 s later, using a Δ⁢t of 0.05 s. (Express your answer in vector form.)

(c) If your answers are different, explain why.

• Assume, as in the example in the book, that the job separation rate s is 0.01 (1%)

  per month and that the job finding rate f is 0.2 (20%) per month.

• Assume that the labor force is 100 million.

  (a) What is the steady state unemployment rate for this economy?

  (b) Given that L = 100 million, what is the steady state number of employed E and unemployed U ?

(c) If U.S. immigration policy changed today (period t = 1) such that we allowed more people to enter the country and L increased to 110 million from its initial value of 100 million. Assume that these new entrants would be unemployed first and then find jobs at the job finding rate f . Create a table (maybe in Excel) that shows how E, U , and U/L evolve over time, givens = 0.01 and f = 0.2, starting at t = 1 and ending when the unemployment rate reaches its steady state rounded to the nearest thousandth.

(d) In the table from the previous scenario, how many periods does it take for the unemployment rate to reach its steady state level rounded to the nearest thousandth?

The sugar content of the syrup in canned peaches is normally distributed. Suppose that the variance is thought to be σ^2=18⁢  (milligrams)^2. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams.

(a) Test the hypothesis H0:σ^2 = 18 versus H1:σ2 ≠ 18 using α = 0.05
Find χ02 .Round your answer to two decimal places (e.g. 98.76).

Is it possible to reject H0 hypothesis at the 0.05 level of significance?

A. Yes

B. No

Find the P-value for this test.

(b) Suppose that the actual standard deviation is twice as large as the hypothesized value. What is the probability that this difference will be detected by the test described in part (a)?

(c) Suppose that the true variance is σ2=40. How large a sample would be required to detect this difference with probability at least 0.90?

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be A. collectively exhaustive. B. the sample space. C. mutually exclusive. D. independent. (b) If event A and event B are as above and event A has probability 0.2 and event B has probability 0.2, then the probability that A or B occurs is ____

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 61 percent BLUE, 21 percent RED, and 18 percent GREEN.

(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

9. Police plan to enforce speed limits by using radar traps at four different locations within the city limits. A person who is speeding on his/her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations (location 1, location 2, location 3, and location 4, respectively). The radar traps at each of the locations (location 1, location 2, location 3, and location 4, respectively) will be operated 40%, 30%, 20%, and 30% of the time. If a randomly selected person received a speeding ticket on his/her way to work, what is the probability that he/she passed through the radar trap located at location 1? (10 points)

Hint: Consider the following five events:

A: a speeding person receives a speeding ticket (note: a speeding person will receive a speeding ticket if the person passes through the radar trap when operated.)

B₁: a speeding person passing through location 1,

B₂: a speeding person passing through location 2,

B₃: a speeding person passing through location 3,

B₄: a speeding person passing through location 4.

Problem 15-05 (Algorithmic)

Consider the following time series data.

1. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.

   Week	Time Series Value	Forecast
   1	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE: ——————
   
   The forecast for week 7: ————————
   
2. Use  = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.

   Week	Time Series Value	Forecast
   1	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE: ————————
   
   The forecast for week 7: ——————
3. Use trial and error to find a value of the exponential smoothing coefficient  that results in a smaller MSE than what you calculated for  = 0.2. Find a value of  for the smallest MSE. Round your answer to three decimal places.
   
   alpha = ——————————

Consider the following IS-LM model with a banking system:

Consumption:

C = 7 + 0.6Y_D

Investment:

I = 0.205Y − i

Government expenditure:

G = 10

Taxes:

T = 10

Money demand: M^d / P = Y / i

Demand for reserves:

R^d = 0.375D^d

Demand for deposits:

D^d = (1 − 0.2)M^d

Demand for currency:

CU^d = 0.2M^d

This says that consumers hold 20% (c = 0.2) of their money as currency and the required reserve ratio is 37.5% (θ = 0.375). Demand for central bank money (H^d) is the total amount of currency being demanded plus the total demand for reserves. Suppose the price level is P = 1 and that the initial supply of central bank money is $100.

1.Solve for the money multiplier. Explain your work.

2.Solve for equilibrium output and the equilibrium interest rate at the initial supply of central bank money (ie. $100).

3.Suppose that the central bank sells $80 worth of bonds using open market operations. Solve for the new equilibrium output.

4.Solve for the the new equilibrium interest rate after the open market operations and use an IS-LM graph to explain what happened.

Consider a residential network that connects to the internet with a DSL link that has a download rate of 4 Mb/s. Assume that there are three UDP flows sharing the link and the remote hosts are sending at rates of 1 Mb/s, 2 Mb/s and 3 Mb/s. Assume that the ISP router has a link buffer that can hold 300 packets (assume all packets have the same length).

a) For each flow, what fraction of the packets it sends are discarded?

b) For each flow, about how many packets does it have in the queue.

c) Now, suppose the queue at the ISP router is replaced by three queues that can each hold 100 packets and that the queues are scheduled using weighted-fair queueing, where the weights are all 0.33. In this case, what fraction of packets are discarded from each flow?

d) How many packets does each flow have in the queue?

e) Now, suppose the weights are 0.2 for the first flow, 0.6 for the second and 0.2 for the third. In this case, what fraction of packets are discarded from each flow?

f) How many packets does each flow have in the queue?