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. What are the appropriate hypotheses one should test?
H₀: μ = 4.06 against   H_a: μ > 4.06.
H₀: μ = 4.06 against   H_a: μ ≠ 4.06.
H₀: μ = 2.33 against   H_a: μ ≠ 2.33.
H₀: μ = 2.33 against   H_a: μ > 2.33.
H₀: μ = 2.33 against   H_a: μ < 2.33.
H₀: μ = 4.06 against   H_a: μ < 4.06.

2. The formula of the test-statistic to use here is
\dfrac[(x)] − μ₀σ/√n.
\dfrac[(x)] − μ₀s/√n.
\dfrac[^(p)] − p₀√{p₀(1−p₀)/n}.
None of the above.

3. Rejection region: We should reject H₀ at 2.5% level of significance if:
test statistic < −1.960.
|test statistic| > 2.241.
test statistic < −2.060.
test statistic > 1.960.
|test statistic| > 2.385.
test statistic > 2.060.

4. The value of the test-statistic is (answer to 3 decimal places):

5. If α = 0.025, what will be your conclusion?
Do not reject H₀.
Reject H₀.
There is not information to conclude.

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

7. We should reject H₀ for all significance level which are
not equal to p-value.
larger than p-value.
smaller than p-value.

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.

4. If α = 0.1, and the p-value is 0.1965, what will be your conclusion?
Do not reject H₀.
Reject H₀.
There is not enough information to conclude.

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.

4. If α = 0.1, , and the p-value is 0.1904, what will be your conclusion?
Reject H₀.
There is not enough information to conclude.
Do not reject H₀.

1. A high-level voltage power supply should have a nominal output voltage of 350 V. A sample of four units is selected each day and tested for process-control purposes. The data (20 days, 1 sample/day) shown in the table below give the difference between the observed reading on each unit and the nominal voltage times ten; that is, x_i = (observed voltage on unit 350)*10.

1. Calculate the UCL and LCL for the x̄-chart.
2. Calculate the UCL and LCL for the R-chart.
3. Set up x̄ and R charts on this process. Is the process in statistical control?
4. If specifications are at 350 V ± 5 V, what can you say about process capability? Calculate C_p. Interpret the calculated value of C_p.
5. Calculate C_pk. Interpret the calculated value of C_pk.

Iterative Merge Sort is not working

#include
#include
#include
int* b;
void merge(int a[], int left, int mid, int right)
{
   int i = left, j = mid + 1, k = left;

   while (i <= mid && j <= right)
   {
       if (a[i] < a[j])
           b[k++] = a[i++];
       else
           b[k++] = a[j++];
   }
   for (; i <= mid; i++)
   {
       b[k++] = a[i];
   }
   for (; j <= right; j++)
   {
       b[k++] = a[j];
   }
   for (int i = left; i <= right; i++)
   {
       a[i] = b[i];
   }

}
void mergesort(int a[], int n)
{
   int p, left, right, mid, i;
   for (p = 2; p <= n; p = p * 2)
   {
       for (i = 0; i + p - 1 < n; i = i + p)
       {
           left = i;
           right = i + p - 1;
           mid = (left + right) / 2;
           merge(a, left, mid, right);
       }
   }
   if (p / 2 < n)
   {
       merge(a, 0, (p / 2) - 1, n - 1);
   }
}
void main()
{
   int max, * a;
   scanf("%d", &max);
   a = (int*)malloc(sizeof(int) * max);
   b = (int*)malloc(sizeof(int) * max);
   for (int i = 0; i < max; i++)
   {
       scanf("%d", &a[i]);
   }
   mergesort(a, max);
   for (int i = 0; i < max; i++)
   {
       printf(" %d", a[i]);
   }
}

input 50

50 49 48 47 46 45 ~ 5 4 3 2 1

output

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19 20 21 22 23 24 ~ 50

why 1,2 are between in 18 and 19?

please answer and correct code

Strong acids and bases completely dissociate in water. classify the following chemical compounds as strong acids, weak acids, strong bases, and weak bases.

1. H2SO4

2. KOH

3. HI

4. HCN

5. H2S

6. KF

7. Be(OH)2

8. NH3

1. What do you understand about DRI's in the past and present?

2. What is the difference between RDA and AMDR?

3. What is a tertiary prevention example of type 2 DM?

4. Plant source of fats ( example of foods)?

5. Animal source of Fats (food examples)?

Which of the following transitions in the Bohr hydrogen atom results in the emission of the shortest wavelength photon.

a. n = 2 → n = 5

b. n = 5 → n = 2

c. n = 6 → n = 3

d. n = 3 → n = 6

e. n = 4 → n = 1

determine the distances between the genes, coefficient of coincidence, and interference. Show all calculations. (create pairs eg wfm and +++ are a parental pair)

1. What is the relationship that constitutes the foundation of the Capital Asset Pricing

Model?

2. What are the vital functions that this relationship serves?

3. List two (2) of the assumptions that lead to the basic version of the CAPM

4. Explain what the “Market Portfolio” is.

5. Explain what the Security Market Line is.