PART 1:

When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field. However, there is a concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 26 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of 2.33 MPa, and a standard deviation of 4 MPa. Orthodontists want to know if the true mean breaking strength is less than 4.06 MPa, the mean breaking strength of the composite adhesive. Assume normal distribution for breaking strength of the new adhesive.

1. The p-value of the test is (answer to 4 decimal places):

PART 2:

Are medical students more motivated than law students? A randomly selected group of each were administered a survey of attitudes toward Life, which measures motivation for upward mobility. The scores are summarized below. The researchers suggest that there are occupational differences in mean testosterone level. Medical doctors and university professors are two of the occupational groups for which means and standard deviations are recorded and listed in the following table.

Let us denote:

• μ₁: population mean testosterone among medical doctors,
• μ₂: population mean testosterone among university professors,
• σ₁: population standard deviation of testosterone among medical doctors,
• σ₂: population standard deviation of testosterone among university professors.

1. If the researcher is interested to know whether the mean testosterone level among medical doctors is higher than that among university professors, what are the appropriate hypotheses he should test?
H₀: μ₁ = μ₂   against   H_a: μ₁ < μ₂.
H₀: μ₁ = μ₂   against   H_a: μ₁ > μ₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ ≠ [(x)]₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ > [(x)]₂.
H₀: [(x)]₁ = [(x)]₂   against   H_a: [(x)]₁ < [(x)]₂.
H₀: μ₁ = μ₂   against   H_a: μ₁ ≠ μ₂.

Case 1: Assume that the population standard deviations are unequal, i.e. σ₁ ≠ σ₂.
1. What is the standard error of the difference in sample mean [(x)]₁ − [(x)]₂? i.e. s.e.([(x)]₁−[(x)]₂) = [answer to 4 decimal places]

2. Rejection region: We reject H₀ at 10% level of significance if:
t < −1.89.
t > 1.41.
t < −1.41.
|t| > 1.89.
t > 1.89.
None of the above.

3. The value of the test-statistic is: Answer to 3 decimal places.

Case 2: Now assume that the population standard deviations are equal, i.e. σ₁ = σ₂.
1. Compute the pooled standard deviation, s_pooled [answer to 4 decimal places]

2. Rejection region: We reject H₀ at 10% level of significance if:
t > 1.78.
t < −1.36.
t > 1.36.
|t| > 1.78.
t < −1.78.
None of the above.

3. The value of the test-statistic is: Answer to 3 decimal places.

What is the conjugate acid of each of the following bases? Write the equilibrium reactions in aqueous solution for each base.
1) Se^2-.
2) HPO₄^2-.
3) ClO3^-.
4) [Co(NH₃)₅(OH)]²⁺.
5) SeO₄^-.

Find the output for the following statements.

• System.out.println(3%2+1+(3/2));

• char ch = 69;
  System.out.println(ch);

• int x = 30;

int y = 4;

double z = x/y;

System.out.println(z);

Use a python code to solve

Use Newton interpolation to find the unique polynomial p2(x) of degree 2 or less, that agrees with the following data: p2(0) = 1, p2(2) = 5, p2(4) = 17.

1. In the EAI sampling problem, the population mean is $51,300 and the population standard deviation is $5,000. When the sample size is n = 30, there is a 0.4161 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

1.1 What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?

1.2 What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?

2. The following data are from a simple random sample. 4, 9, 12, 7, 12, 16

2.1 What is the point estimate of the population mean?

2.2 What is the point estimate of the population standard deviation (to 1 decimal)?

3. Suppose a random sample of size 53 is selected from a population with = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

3.1 The population size is infinite (to 2 decimals).

3.2 The population size is N = 50,000 (to 2 decimals).

3.3 The population size is N = 5,000 (to 2 decimals).

3.4 The population size is N = 500 (to 2 decimals).

4. A population has a mean of 400 and a standard deviation of 60. Suppose a sample of size 100 is selected and is used to estimate . Use z-table.

4.1 What is the probability that the sample mean will be within +/- 7 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

4.2 What is the probability that the sample mean will be within +/- 12 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

For the rest of the lab, you will make the assumption that your data is approximately normally distributed. Use Excel to answer the following questions for the Net Sales data. Copy and paste the output below, don’t include as a separate file, make sure your x axis is labelled properly. You will have to “insert” your graphs in the appropriate places below. Please don’t upload more than one file for me to open and grade, your entire lab should be in ONE uploaded file. If you can’t do that, then print out the separate files and then scan it in as one file, but you should be able to figure out how to copy and paste all your answers into one document.

Locate your middle x value (M) and your highest x value (H) on the axis.

Shade the area between x=M and x=H.

Find the value of the shaded area under the curve. In other words, what is P(M< x<H)?

The following table shows the MB of polluting to firm A and firm B (which represents the MC of abatement of pollution to the firms)

A. Imagine an environmental standard where each firm is allowed to emit 11 units. 1. What is the total cost of this standard to firm A? Firm B? 2. What is the total cost to the industry made up of these two firms?

B. Now suppose that a tax of $24 per unit of emissions is imposed. 1. How many units of emissions will firm A choose to emit? Firm B? 2. What is the total cost to this industry for the reduction in emissions?

C. Now suppose each firm is issued 11 permits in a tradable emissions permits market. 1. Who will purchase permits? Who will sell? 2. Where will the price of permits sell?

Assume that U.S. can produce two goods, compact discs and apples. Compact discs are produced using capital and labor. Apples are produced using land and labor. The total supply of labor is 20 workers. Given the supply of capital, the marginal products of labors are as follows:

Suppose that the price of a compact disc is $2 and the price of apples is $1

The equilibrium allocation of labor between the compact disc sector (L_CD) and the apple sector (L_A) is respectively

B)

Suppose that the price of a compact disc is $2 and the price of apples is $1

The equilibrium wage rate (w) is

What is time Complexity each of the following function?

1-

void function(int n)

{

            for (int i=n/2; i<=n; i++)  

                        for (int j=1; j<=n/2; j++)

                                    for (int k=1; k<=n; k = k * 2)

                                                print ”Hello”;

}

2-

void function(int n)

{

            for (int i=n/2; i<=n; i++)  

                        for (int j=1; j<=n; j = 2 * j)

                                    for (int k=1; k<=n; k = k * 2)

                                                print ”Hello”;

}

3-

void function(int n)

{

            for (int i=1; i<=n; i++)  

                        for (int j=1; j<=n; j = j + i)  

                                                print ”Hello”;

}

4-

Int n=2^{2^k}

for (int i=1; i<=n; i++)

{

             J=2

            While(j<=n)

            {

                        j=j²

                        print ”Hello”;

            }

}

5=

If n>=2

While(n>1)

{

            n=n/2;

            print ”Hello”;

}

P&L is a profit-maximizing shirt manufacturing firm. The firm can sell all the shirts it can produce to retailers at a price of $20 each. P&L can hire all of the workers it wants at a market wage of $120 per day per worker. The table below shows the firm’s short-run production function.

Answer the following based on the above information

What is the marginal physical product of the 5th worker?

choices:

10

15

25

12

Next question:

Refer to the chart in Question #1.

After what worker does Diminishing Marginal Product occur?

a.1

b.2

c.3

d.4

3.

Refer to the chart in Question #1: Calculate the marginal revenue product (VMPL) of the third worker.

Group of answer choices

400

300

160

100

4.

Refer to the chart in Question 1: How many workers should the firm hire to maximize profit

Group of answer choices

8

7

6

5

5.

Refer to the chart in Question #1: If the price of shirts decreased to $15 and the wage per day of workers increased to $150, how many workers would be hired due to this change?

Group of answer choices

2

4

6

5