. 1. In the Operating System zoo describe the 4 different types of Operating Systems and describe them.

2. What is a process, when are they created and when are they terminated.

1. Consider sample data with

• = 20 and
• s = 4.

(For each answer, enter an exact number.)

(b) Compute a 75% Chebyshev interval around the sample mean.
Lower Limit =
Upper Limit =

2. How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

(a)

Make a scatter diagram of the data and visualize the line you think best fits the data. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

(b)

Would you say the correlation is low, moderate, or strong?

lowmoderate    strong

Would you say the correlation is positive or negative?

positive or negative    

(c)

Use a calculator to verify that Σ(x) = 57, Σ(x²) = 869, Σ(y) = 644, Σ(y²) = 93,166, and Σ(x y) = 8,748.

Compute r. (Enter a number. Round your answer to three decimal places.)


As x increases from 3 to 22 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to remain constant as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.    Given our value of r, y should tend to increase as x increases.Given our value of r, y should tend to decrease as x increases.

The Sun radiates energy at a rate of about 4 × 1026 W.

1) At what distance from the Sun is its intensity the same as that of a 100 W light bulb 1 m away from you?

2) How does that compare to the distance between the Sun and the Earth?

3) Between which 2 planets’ orbits does this distance lie?

Prove that the set of all subsets of {1, 4, 9, 16, 25, ...} is uncountable.

1. Consider a multinomial experiment with n = 307 and k = 4. The null hypothesis to be tested is H₀: p₁ = p₂ = p₃ = p₄ = 0.25. The observed frequencies resulting from the experiment are: (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Choose the appropriate alternative hypothesis.

• Not all population proportions are equal to 0.25.

• All population proportions differ from 0.25.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

• p-value   0.10
• 0.01  p-value < 0.025

• p-value < 0.01

• 0.025  p-value < 0.05
• 0.05  p-value < 0.10

c. At the 10% significance level, what is the conclusion to the hypothesis test?

• Reject H₀ since the p-value is less than the significance level.

• Reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is greater than the significance level.

• Do not reject H₀ since the p-value is less than the significance level.

2. An analyst is trying to determine whether the prices of certain stocks on the NASDAQ are independent of the industry to which they belong. She examines four industries and, classifies the stock prices in these industries into one of three categories (high-priced, average-priced, low-priced).

a. Choose the competing hypotheses to determine whether stock price depends on the industry.

• H₀: Stock price is independent of the industry.; H_A: Stock price is dependent on the industry.

• H₀: Stock price is dependent on the industry.; H_A: Stock price is independent on the industry.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

• p-value < 0.01

• 0.01 p-value < 0.025

• 0.025  p-value < 0.05
• 0.05 p-value < 0.10
• p-value  0.10

c. At a 1% significance level, what can the analyst conclude?

• Do not reject H₀; there is not enough evidence to support the claim that the stock price is dependent on the industry.

• Reject H₀; there is enough evidence to support the claim that the stock price is dependent on the industry.

• Reject H₀; there is not enough evidence to support the claim that the stock price is dependent on the industry.

• Do not reject H₀; there is enough evidence to support the claim that the stock price is dependent on the industry.

3. Using 20 observations, the multiple regression model y = β₀ + β₁x₁ + β₂x₂ + ε was estimated. A portion of the regression results is shown in the accompanying table:

a. At the 5% significance level, are the explanatory variables jointly significant?

• No, since the p-value of the appropriate test is less than 0.05.

• Yes, since the p-value of the appropriate test is more than 0.05.

• Yes, since the p-value of the appropriate test is less than 0.05

• No, since the p-value of the appropriate test is more than 0.05.

b. At the 5% significance level, is each explanatory variable individually significant?

• Yes, since both p-values of the appropriate test are less than 0.05.

• Yes, since both p-values of the appropriate test are more than 0.05.

• No, since both p-values of the appropriate test are not less than 0.05.

• No, since both p-values of the appropriate test are not more than 0.05.

c. What is the likely problem with this model?

• Multicollinearity since the standard errors are biased.

• Multicollinearity since the explanatory variables are individually and jointly significant.

• Multicollinearity since the explanatory variables are individually significant but jointly insignificant.

• Multicollinearity since the explanatory variables are individually insignificant but jointly significant.

4. The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008.

a-1. Estimate the model: Salaryˆ=Salary^= β₀ + β₁ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.)

a-2. Interpret the coefficient of ERA.

• A one-unit increase in ERA, predicted salary decreases by $2.89 million.

• A one-unit increase in ERA, predicted salary increases by $2.89 million.

• A one-unit increase in ERA, predicted salary decreases by $11.48 million.

• A one-unit increase in ERA, predicted salary increases by $11.48 million.

b. Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.31. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)

Apex Inc. produces gadgets. Its production function is ? = min(4?, ? − 1), for ? ≥ 0 and ? ≥ 1, where ? denotes units of capital input, ? denotes units of labor input, and ? denotes units of output. (Note that ? = 0 for all ? < 1.) The price of a unit of capital input is ? and the price of a unit of labor input is ?.

a. Find Apex’s ??? and ??? functions.

b. Find Apex’s ??? function.

c. Suppose that ? = 8 in the short run. Find Apex’s short run (contingent) demand function for labor input. (Hint: This will be a function of the target output level, ?.)

d. Suppose that ? = 8 in the short run. Find Apex’s short run total cost function. (Hint: This will be a function of the target output level, ?, and the input prices, ? and ?.)

e. Find Apex’s long run (contingent) demand functions for labor input and capital input. (Hint: These will be functions of the target output level, ?, but not the input prices, ? and ?. Why?)

f. Find Apex’s long run total cost function. (Hint: This will be a function of the target output level, ?, and the input prices, ? and ?.)

For questions 1-4, you will be provided with a t-value, the number of degrees of freedom, alpha, and whether the test is one- or two-tailed. You will then be asked to establish the critical t-value and state your decision regarding the null hypothesis.

1. t = 1.45, df = 12, alpha = .05, two-tailed

   critical value of t =
   Decision =

   (2 points)

2. t = 2.90, df = 22, alpha = .01, two-tailed

   critical value of t =
   Decision =

   (2 points)

3. t = 2.60, df = 17, alpha = .05, one-tailed

   critical value of t =
   Decision =

   (2 points)

4. t = 1.70, df = 13, alpha = .05, one-tailed

   critical value of t =
   Decision =

Solve the differential equation by variation of parameters.

y'' + 3y' + 2y =

y(x) =

What is the present value of the cost of college education for 4 children ages 1, 3, 5, and 7. The current cost of college is $25,000. The children will begin college at age 18 and be in college for 4 years. Education inflation is expected to be 6% and the parents portfolio rate of return is 8%.

4 charges are fixed to the corners of a square of side .53 cm. Charge 1 of -1 uC is fixed to the top left corner. Charge 2 of -2uC is fixed to the top right corner, charge 3 of 3uC is fixed to the bottom left corner , and charge 4 of -4uC is fixed to the bottom right corner. a) find the magnitude and direction of the electric field at the center of the square b) find the potential at the center c) find the electric potential energy of the system.