(Using R)Consider a hardness testing machine that presses a rod with a pointed tip into a metal specimen with a known force. By measuring the depth of the depression caused by the tip the hardness of the specimen is determined. Four tips and four test coupon are available and following data are observed

1. Analyze the data from this experiment
2. Perform a test to make comparisons among the four tips to determine specifically which tips differ in mean hardness readings.

1. Two acoustical waves are incident on one point after traversing different paths. The two waves are characterized by the following amplitude variations

p1=0.5sin( 2πx1-684πt )Pa,

p2=0.5sin( 2πx2-684πt+α )Pa,

1. Derive an expression for the resultant pressure.

2. What is the frequency and wavelength of these two waves?

3. For t=2.924 ms, what are the resultant amplitudes for x1=x2=1 m, for α=0, α=4, and α=π/2 radians?

4. For t=2.924 ms, what are the resultant amplitudes when x1=1.25 m and x2=1 m, for α=0, α=π/4, and α=π/2 radians?

Error Degrees of Freedom are calculated as n - p - 1 for multiple regression models. The p represents the number of coefficients (not including the intercept) in the estimated model. Part A: Report the Error Degrees of Freedom for this example: Assume 160 observations are used to estimate a model with 2 numerical explanatory variables both with a linear relationship to the response and 1 categorical explanatory variable. The categorical variable has 4 levels. Part B: Assume 160 observations are used to estimate a model with 2 numerical explanatory variables both with a linear relationship to the response. In addition there is one categorical variable with 3 levels and another categorical variable with 4 levels. Report the Error Degrees of Freedom

Compute the Discounted Payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 14 percent and the maximum allowable discounted payback is 3 years.

Compute the PI statistic for Project X and note whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 11 percent.

Paul's Pizzeria as signed a new five year lease for 1,000 SF of restaurant space in a shopping center in Granada Hills. The base rent on the lease is $3.00/SF, NNN with 3% annual rent increases to account for inflation. However, the lease has a percentage lease clause, that states the lessee will pay an additional 3% of gross annual sales over $1,200,000. Gross sales for the tenant are estimated to be as follows:

Year 1 - $ 1,200,000

Year 2 - $ 1,100,000

Year 3 - $ 1,400,000

Year 4 - $ 1,090,000

Year 5 - $ 1,500,000

What are the estimated annual lease payments for:

Year 1 ?

Year 2 ?

Year 3 ?

Year 4?

Year 5 ?

Show me how it is done in Excel if possible:

A store has one counter. The probability of inter-arrival time (in min) and service time (in min.) of customers are given in the following table.

Distribution of time between Arrival

Distribution of Service-Time

Journalize the following business transactions in general journal form. Identify each transaction by number.

(Credit account titles are automatically indented when the amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.)

For long run economics growth it is nesassry to maintain?

1 convergence
2 conditional convergence
3 divergence
4 semi- conditional convergence

The sum of marginal propensity to consume and marginal propensity to save is always
A 3
B 2
C 1
D 0

Is developing countries, marginal propensity to consume is

A low
B sometimes high
C high
D sometimes low

In Richard quivalance mechanism of 4 year
Government wants to hold

A bond
B coupon payment
C note
D bill

A fall in domestic consumption will make the import
A. cannot determine the information
B. Rise
C. Sometime fall and sometimes rise
D. Fall

Comparing Investment Criteria. Consider the following two mutually exclusive design projects using a required return of 18%:

1. Find the NPV for both projects a and b. (round to second decimal)

2. Find the IRR for both projects a and b. (round to secound decimal)

3. Find the PI for both projects A and B. (round to second decimal)

4. To maximize shareholder's wealth, I would chose project____?

* using a financial calculator please show and explain work.

Thank you

Results from the last four samples from a process are shown in the table. Calculate control limits for an R and X chart. Determine whether the process is in statistical control.

To control the lead time of a process, samples of size ten are taken from the process. If the average time to complete the process is three days, with a standard deviation of 0.5 days. Calculate the control limits for an X chart at 3 sigma level.