Two payment plans are considered. Plan A pays $100 immediately, $200 in 2 years and $100 in 3 years. Plan B simply pays $350 immediately.

(a) Compare the present values of Plan A and Plan B at 7.8% and 8.5% effective interest rate per year.

(b) Assume Plan A is purchased for $350 at the time of the first payment.

Prove the existence of a unique yield rate which lies between 7.8% and 8.5%.

(c) Using a single iteration of linear interpolation between 7.8% and 8.5%, find an approximate yield rate.

PRESENT VALUE OF AN ANNUITY

Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent.

1. $700 per year for 16 years at 6%.

   $  

2. $350 per year for 8 years at 3%.

   $  

3. $800 per year for 6 years at 0%.

   $  

   Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

4. $700 per year for 16 years at 6%.

   $  

5. $350 per year for 8 years at 3%.

   $  

6. $800 per year for 6 years at 0%.

   $  

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $700 per year for 16 years at 8%.

   $  

2. $350 per year for 8 years at 4%.

   $  

3. $200 per year for 8 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $700 per year for 16 years at 8%: $  

   Present value of $350 per year for 8 years at 4%: $  

   Present value of $200 per year for 8 years at 0%: $  

Tom's Shoe Repair provides a variety of shoe repair services. Analysis of monthly costs revealed the following cost formulas when direct labor hours are used as the basis of cost determination:

Supplies: y=$0+$4.00X

Production supervision and direct labor: y=$500+$7.00X

Utilities: y=$350+$5.40X

Rent: y=$450+$0.00X

Advertising: y=$75+$0.00X

a. Prepare a flexible budget 250, 300, 350, and 400 direct labor hours.

b. Calculate a total cost per direct labor at each level of activity.

c. Tom's employees usually work 350 direct labor hours per month. The average shoe repair requires 1.25 labor hours to complete. Tom wants to earn a 40 percent margin on his cost. What should be the average charge per customer, rounded to the nearest dollar to achieve Tom's profit objective?

*Don not use excel or any other software to solve this problem

The 30 Major League Baseball teams are divided into two "leagues" of 15 teams each: the American League and the National League. A random sample of 55 American League players and a random sample of 55 National League players were selected. The sample mean and standard deviation of the salaries of the sampled players is shown in the table below.

Note: The degrees of freedom for this problem is df = 100.103603. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. A statistically-minded baseball fan wants to use statistical inference to determine if the salaries of the players in the American League are different from the salaries of the players in the National League. Select the appropriate hypotheses for this research question.
A. ?0H0: ?1μ1 = ?2μ2 vs.  ??HA: ?1μ1 < ?2μ2
B. ?0H0: ?1μ1 = ?2μ2 vs.  ??HA: ?1≠μ1≠ ?2μ2
C. ?0H0: ?1μ1 = ?2μ2 vs.  ??HA: ?1μ1 > ?2μ2

2. Calculate the appropriate test statistic.  ? z t X^2 F  =

3. Calculate the p-value.

4. Construct a 99% confidence interval for the difference in American League and National League salaries, ?????????μAmerican - ?????????μNational. ( ,  )

The 30 Major League Baseball teams are divided into two "leagues" of 15 teams each: the American League and the National League. A random sample of 48 American League players and a random sample of 48 National League players were selected. The sample mean and standard deviation of the salaries of the sampled players is shown in the table below.

Note: The degrees of freedom for this problem is df = 93.631761. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. A statistically-minded baseball fan wants to use statistical inference to determine if the salaries of the players in the American League are different from the salaries of the players in the National League. Select the appropriate hypotheses for this research question.
A. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 > ?2μ2
B. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 < ?2μ2
C. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1≠μ1≠ ?2μ2

2. Calculate the appropriate test statistic.  ? z t X^2 F  =

3. Calculate the p-value.

4. Construct a 90% confidence interval for the difference in American League and National League salaries, ?????????μAmerican - ?????????μNational. ( ,  )

The 30 Major League Baseball teams are divided into two "leagues" of 15 teams each: the American League and the National League. A random sample of 49 American League players and a random sample of 49 National League players were selected. The sample mean and standard deviation of the salaries of the sampled players is shown in the table below.

Note: The degrees of freedom for this problem is df = 94.452867. Round all results to 4 decimal places. Remember not to round for intermediate calculations!

1. A statistically-minded baseball fan wants to use statistical inference to determine if the salaries of the players in the American League are different from the salaries of the players in the National League. Select the appropriate hypotheses for this research question.
A. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1≠μ1≠ ?2μ2
B. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 < ?2μ2
C. ?0H0: ?1μ1 = ?2μ2 vs. ??HA: ?1μ1 > ?2μ2

2. Calculate the appropriate test statistic.  ? z t X^2 F  =

3. Calculate the p-value.

4. Construct a 99% confidence interval for the difference in American League and National League salaries, ?????????μAmerican - ?????????μNational. ( ,  )

The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization's membership is listed below.

1. Find the mean, median, and standard deviation of the number of members per component. (Round your answers to 2 decimal places.)
2. Find the coefficient of skewness, using the software method. (Round your answer to 2 decimal places.)
3. Determine the first and third quartiles. Do not use the method described by Excel. (Round your answers to 2 decimal places.)

4. What are the limits for outliers? (Round your answers to the nearest whole number. Negative amounts should be indicated by a minus sign.)

i)prove that a cylindrical co-ordinate system is orthogonal.                                     iii) Express the velocity v and acceleration of a particle in cylindrical co-ordinates.                                                   iii) find the square of the element of arc length in cylindrical co-ordinates and determine the corresponding scale factors.                                                           iv) The transformation from retangular to cylindrical co-ordinates is defined by the transformation:.                                   x=pcos#,y=psin#, z=z                                    find the Jacobian of the transformation

a) Perform a statistical test to see whether the average loans of customers before the change at the Bank of America and Wells Fargo are different.

Loans before the change at Bank of America:  

51.2
46.1
43.4
44.1
50.2
39.1
35.6
49.3
37.4
49.3
52.9
50.0
37.7
53.0
45.7
36.9
43.4
41.2
54.9
55.0
36.8
38.6
37.1
49.9
47.2
46.0
39.9
53.9
35.5
54.3
36.8
42.0
50.5
50.3
44.7
37.6
35.3
39.8
48.7
51.5

Loans before the change at Wells Fargo:

50.4
42.9
52.2
44.7
40.6
38.2
46.6
47.0
53.5
36.5
47.7
45.8
44.5
38.3
54.3
54.5
44.5
42.4
52.3
50.7
43.7
54.5
38.7
44.5
52.5
53.0
48.6

Increase in loans at BoA:

12.2
8.4
1.3
13.2
5.5
7.4
14.0
-5.1
23.2
7.2
-3.9
12.8
23.7
-2.4
-1.0
7.8
6.7
18.0
-0.1
0.4
8.9
20.5
18.1
9.6
-1.3
1.2
18.5
4.2
28.0
8.7
24.2
5.4
-6.1
13.4
5.0
20.4
13.5
17.4
14.8
-7.9
Increase in loans at Wells Fargo

4.5
16.1
5.0
7.5
19.3
10.0
12.9
11.3
5.1
20.1
14.4
13.1
13.3
10.3
-5.1
-2.1
18.4
13.9
10.3
-4.8
17.3
-1.9
6.9
12.3
0.8
-5.7
10.1
8.2

b) Construct a 95% confidence interval for the difference of average loans of customers before the change at the Bank of America and Well Fargo branch.