Ehrlich Co. began business on January 2, 20Y8. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in 20Y9, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed.

None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5%. Data on dates of employment, salary rates, and employees’ income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:

Required:

1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2) for 20Y8.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee’s earnings; (d) federal unemployment compensation at 0.6% on the first $10,000 of each employee’s earnings; (e) total.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

Wage and Tax Statement Data on Employer FICA Tax

Ehrlich Co. began business on January 2, 20Y8. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in 20Y9, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed.

None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5%. Data on dates of employment, salary rates, and employees’ income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:

Required:

1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2) for 20Y8.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee’s earnings; (d) federal unemployment compensation at 0.6% on the first $10,000 of each employee’s earnings; (e) total.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

Ehrlich Co. began business on January 2. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in the following year, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed.

None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5% on salary. Data on dates of employment, salary rates, and employees' income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:

Required:

1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2). Enter amounts to the nearest cent if required. Enter all amounts as positive numbers.

2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee's earnings; (d) federal unemployment compensation at 0.8% on the first $10,000 of each employee's earnings; (e) total. Round your answers to two decimal places.

Ehrlich Co. began business on January 2, 20Y8. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in 20Y9, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed.

None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5%. Data on dates of employment, salary rates, and employees’ income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:

Required:

1.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee’s earnings; (d) federal unemployment compensation at 0.6% on the first $10,000 of each employee’s earnings; (e) total.

Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2) for 20Y8.

(10 pts) Suppose that when I drive to school, I encounter one traffic light on Lewis Road and one traffic light on Santa Rosa Rd. Let the random variable X = number of red lights that I encounter on Lewis and Y = number of red lights that I encounter on Santa Rosa. Suppose that the marginal distributions of X and Y are as shown in the following probability table:

X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0
Notice that E(X) = E(Y) = .5, and Var(X) = Var(Y) = .25.

a) Fill in the table in such a way that Corr(X,Y) = 1. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0


b) Fill in the table in such a way that Corr(X,Y) = -1. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0


c) Fill in the table in such a way that Corr(X,Y) = 0. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0

Consider the variable W=X+Y, representing the total number of red lights I encounter on my drive to school.
d) Calculate E(W)





e) For each of the cases in parts a), b) and c), calculate SD(W)

1. (10pt) Let V and W be a vector space over R. Show that V × W together with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ∈V, w0,w1 ∈W

   and

   λ·(v,w)=(λ·v,λ·w) for λ∈R, v∈V, w∈W is a vector space over R.

2. (5pt)LetV beavectorspaceoverR,λ,μ∈R,andu,v∈V. Provethat (λ+μ)(u+v) = ((λu+λv)+μu)+μv.

   (In your proof, carefully refer which axioms of a vector space you use for every equality. Use brackets and refer to Axiom 2 if and when you change them.)

1. Determine if the following statements are true or false. If a statement is true, prove it in general, If a statement is false, provide a specific counterexample.

Let V and W be finite-dimensional vector spaces over field F, and let φ: V → W be a linear transformation.

A) If φ is injective, then dim(V) ≤ dim(W).

B) If dim(V) ≤ dim(W), then φ is injective.

C) If φ is surjective, then dim(V) ≥ dim(W).

D) If dim(V) ≥ dim(W), then φ is surjective.

E) If V = {0} , then φ is injective.

F) If dim(V) NOT= dim(W), then φ is not bijective.

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A professor thinks that the mean number of hours that students study the night before a test is 1.75. He selected a random sample of 12 students and found that the mean number of study hours was 2.44 and the standard deviation is 1.26 hours. Test the professor’s claim at α = 0.01.

a 1-6) Give the hypotheses for H₀ (a1, a2 and a3) and H1 (a4, a5 and a6)

H₀
a1) µ or p

a2) =, ≥, ≤

a3) number

H₁
a4) µ or p

  
a5) ≠, >, <

  
a6) number

b) Calculate the test statistic. t = _______ (Round your answer to 3 decimals.)

c 1-3) Formulate the decision rule for the p value approach.

Reject H₀ if (c1,c2,c3)
c1) t or p

c2) > or <

  
c3) number

d 1-2) Give the p value (d1 − round to 2 decimals) < p < (d2 - round to 2 decimals) and make a decision (d3).
d1)

  
d2)

  
d3) reject Ho or do not reject Ho

Reject HoDo not reject HoClick for List  

e1-2) Give your conclusion. At α = .___, there (is/is not) enough evidence to conclude that the mean number of hours that students study the night before a test is not 1.75.

e1)

  
e2) is or is not