Calculate the NPV for the following projects. Round PVF values in intermediate calculation to four decimal places. Round answers to two decimal places. Use a minus sign to indicate a negative NPV.

1. An outflow of $7,000 followed by inflows of $3,000, $2,500, and $3,500 at one-year intervals at a cost of capital of 7%.
   $
   
2. An initial outlay of $35,400 followed by inflows of $6,500 for three years and then a single inflow in the fourth year of $18,000 at a cost of capital of 13%. (Recognize the first three inflows as an annuity in your calculations.)
   $
   
3. An initial outlay of $27,500 followed by an inflow of $3,000 followed by five years of inflows of $5,500 at a cost of capital of 9%. [Recognize the last five inflows as an annuity, but notice that it requires a treatment different from the annuity in part (b).]
   $

Suppose that the term structure of interest rates is flat in England and Germany. The GBP interest rate is 4% per annum and the EUR rate is 3% per annum. In a swap agreement, a financial institution pays 9% per annum in GBP and receives 7% per annum in EUR. The exchange rate between the two currencies has changed from 1.1 EUR per GBP to 1.15 EUR per GBP since the swap’s initiation. The principal in British pounds is 20 million GBP. Payments are exchanged every year, with one exchange having just taken place. The swap will last three more years. What is the value of the swap to the financial institution in terms of euros? Assume all interest rates are continuously compounded.

Suppose that the term structure of interest rates is flat in England and Germany. The GBP interest rate is 4% per annum and the EUR rate is 3% per annum. In a swap agreement, a financial institution pays 9% per annum in GBP and receives 7% per annum in EUR. The exchange rate between the two currencies has changed from 1.1 EUR per GBP to 1.15 EUR per GBP since the swap’s initiation. The principal in British pounds is 20 million GBP. Payments are exchanged every year, with one exchange having just taken place. The swap will last three more years. What is the value of the swap to the financial institution in terms of euros? Assume all interest rates are continuously compounded.

3. An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treatedsheep 18, 43, 28, 50, 16, 32, 13, 35, 38, 33, 6, 7

Untreatedsheep 40, 54, 26, 63, 21, 37, 39, 23, 48, 58, 23, 39

1. Construct a 98% confidence interval for the difference of the worm count in a lamb.
2. Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.
3. What are your assumptions that you assumed in part (b)?

An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treatedsheep 18 43 28 50 16 32 13 35 38 33 6 7

Untreatedsheep   40 54 26 63 21 37 39 23 48 58 23 39

(a) Construct a 98% confidence interval for the difference of the worm count in a lamb.

(b) Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.

(c) What are your assumptions that you assumed in part (b)?

An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treated sheep 18, 43, 28, 50, 16, 32, 13, 35, 38, 33, 6, 7

untreated sheep 40, 54, 26, 63, 21, 37, 39, 23, 48, 58, 23, 39

(a) Construct a 98% confidence interval for the difference of the worm count in a lamb.

(b) Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.

(c) What are your assumptions that you assumed in part (b)

1. Use the XLMiner Analysis ToolPak to find descriptive statistics for Sample 1 and Sample 2. Select "Descriptive Statistics" in the ToolPak, place your cursor in the "Input Range" box, and then select the cell range A1 to B16 in the sheet. Next, place your cursor in the Output Range box and then click cell D1 (or just type D1). Finally make sure "Grouped By Columns" is selected and all other check-boxes are selected. Click OK. Your descriptive statistics should now fill the shaded region of D1:G18. Use your output to fill in the blanks below.

   Sample 1 Mean:  (2 decimals)

   Sample 1 Standard Deviation:  (2 decimals)

   Sample 2 Mean:  (2 decimals)

   Sample 2 Standard Deviation:  (2 decimals)

2. Use a combination of native Excel functions, constructed formulas, and the XLMiner ToolPak to find covariance and correlation.

   In cell J3, find the covariance between Sample 1 and Sample 2 using the COVARIANCE.S function.

   (2 decimals)

   In cell J5, find the correlation between Sample 1 and Sample 2 using the CORREL function.
   (2 decimals)

   In cell J7, find the correlation between Sample 1 and Sample 2 algebraically, cov/(sx*sy), by constructing a formula using other cells that are necessary for the calculation.

   (2 decimals)

   Use the XLMiner Analysis ToolPak to find the correlation between Sample 1 and Sample 2. Place your output in cell I10.

   (2 decimals)

3. Calculate z-scores using a mix of relative and absolute cell references. In cell A22, insert the formula =ROUND((A2-$E$3)/$E$7,2). Next grab the lower-right corner of A22 and drag down to fill in the remaining green cells of A23 to A36. Note how the formula changes by looking in Column D. Changing a cell from a relative reference such as E3 to an absolute reference such as $E$3 means that cell remains "fixed" as you drag. Therefore the formula you entered into A22 takes each data observation such as A2, A3, A4..., subtracts $E$3 and then divides by $E$7. Since the last two cells have absolute references they will not change as you drag. The ROUND function simply rounds the z-score to two digits.

   Now find the z-scores for Sample 2 using the same method you learned above by editing the formula to refer to the correct cells for Sample 2. Make sure each z-score is rounded to 2 places.

   Sample 2 z-scores

Riverbend City online news advertises that it is read longer than the national news. The mean for national news is 8 hours per week. The following sample of the Riverbend City online news readers is: 5, 7, 6, 2, 4, 8, 5, 4, 18, 21, 8, 7, 4, 5, 6.

a. State the nondirectional hypothesis. Riverbend City online does not read for 8 hours

b.     State the critical t for a = .05 (two tails).

c.     Answer the following: Is the length of viewing for Riverbend City online news significantly different than the population mean? Explain.

d. Calculate the 95% confidence interval with population mean of 8.

**Need help with b, c, d and is a correct?

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

State the decision for the main effect of the time of day.

Retain the null hypothesis or Reject the null hypothesis.    

State the decision for the main effect of intensity.

Retain the null hypothesis or Reject the null hypothesis.    

State the decision for the interaction effect.

Retain the null hypothesis or Reject the null hypothesis.    

(b) Compute Tukey's HSD to analyze the significant main effect.

The critical value is_________ for each pairwise comparison.

Summarize the results for this test using APA format.