Tommy is examining some risk-free Singapore government securities. The yields to maturity on three government bonds with maturities of 1, 2 and 3 years are respectively 3%, 4% and 6%. The bonds all pay an annual coupon and have the same coupon rate of 1% and a face value of $1,000. (a) Calculate the prices of the three (3) bonds. (b) (i) Calculate the expected 1-year interest rate for year 2. (ii) Calculate the expected 1-year interest rate for year 3

Evaluate the following expressions.

a. Summation from k equals 1 to 18 k

b. Summation from k equals 1 to 7 left parenthesis 4 k plus 1 right parenthesis

c. Summation from k equals 1 to 6 k squared

d. Summation from n equals 1 to 8 left parenthesis 1 plus n squared right parenthesis

e. Summation from m equals 1 to 4 StartFraction 5 m plus 5 Over 7 EndFraction

f. Summation from j equals 1 to 3 left parenthesis 3 j minus 7 right parenthesis

g. Summation from k equals 1 to 8 k left parenthesis 7 k plus 6 right parenthesis

h. Summation from n equals 0 to 4 sine StartFraction n pi Over 2 EndFraction

The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1) is the square footage, the second independent variable (x2) is the number of bedrooms, and the third independent variable (x3) is the age of the house.

Step 1 of 2 :  

Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Step 2 of 2:

Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

It is reported in USA Today that the average flight cost nationwide is $442.28. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually greater than $442.28. What are the appropriate hypotheses for this test?

Question 1 options:

Question 2 (1 point)

In the year 2000, the average vehicle had a fuel economy of 23.13 MPG. You are curious as to whether the average in the present day is greater than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 23.13, Alternative Hypothesis: μ > 23.13. A random sample of 43 vehicles shows an average economy of 24.15 MPG with a standard deviation of 6.69 MPG. What is the test statistic and p-value for this test?

Question 2 options:

Question 3 (1 point)

Consumers Energy states that the average electric bill across the state is $41.553. You want to test the claim that the average bill amount is actually greater than $41.553. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 41.553, Alternative Hypothesis: μ > 41.553. A random sample of 47 customer's bills shows an average cost of $43.307 with a standard deviation of $8.0202. What is the test statistic and p-value for this test?

Question 3 options:

Question 4 (1 point)

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is different from 8.7 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 8.7, Alternative Hypothesis: μ ≠ 8.7. If the researcher takes a random sample of patients and calculates a p-value of 0.0197 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 4 options:

Solve the equations
(a) log₂ x + log₄ x + log₁₆ x=7

(b) 5e^2x+4 =8

(c) 2 + log V1 + x + 3log V1 - x = log V1 - x²

(d) 4^{5 - 9x} = 1 / 8^x-2

a) Using the empirical rule, 95% of female promotional customer ages should be between what two values? Either show work or explain how your answer was calculated.

b)Using the empirical rule, 68% of items purchased should be between what two values? Either show work or explain how your answer was calculated.    

Part 3: Anagram Arranger (20 pts)

Overview

• Create a file called Anagram.java, which reads a series of words input from a file.
• For each word read from the file, the user will have the option to swap letters within that word.
• You are required to use your doubly-linked list class to receive credit for this part of the assignment.
• Therefore, your word should be stored as a List of Characters or Strings (each String being one letter).
• After the user has rearranged the word, it should be written to a file, including the changes the user has made.

Specifications

• The program should welcome the user with the message Welcome to the Anagram Arranger!
• It should then prompt the user to enter the name of a file.
• Provided the user enters a correct file name (see section regarding error checking below), then the program will read in all of the words in the file, one-by-one.
• Each word should be stored in a List of Characters or Strings (each String being one letter).
• It will display the word, along with its corresponding number, with the message:  Word #<count> is <word>
• See below for examples.
• The user will then be prompted to enter the position of two different letters in the word that the user wants to be swapped.
• The program will verify the user choice by re-printing the word with carrots beneath the selected letters.
• The user will then be required to confirm his or her choice with the message: Enter the position numbers of the two letters you wish to swap:
  • The program should accept four different input options from the user -- y, Y, yes, and Yes -- to indicate consent.
• If the user indicates "no", the word will be reprinted with a prompt to enter the position of two different letters.
• If the user enters yes, then the program should swap the two selected letters, and then prompt the user to indicate whether he or she would like to swap additional letters in the word.
  • The program should accept four different input options from the user -- y, Y, yes, and Yes -- to indicate consent.
• The user should be able to continue swapping letters indefinitely.
• Once the user no longer wishes to swap, the current version of the word should be written to a file named output.txt
• Please see below for an incomplete example run:

Welcome to the Anagram Arranger!

Please enter the name of your input file: spooky.txt

Word #1 is zombie
1: z
2: o
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 1 2

z o m b i e
^ ^  
Are these the letters you wish to swap? (y/n): y

The new word is: o z m b i e

Want to keep rearranging? (y/n): y

1: o
2: z
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 3 5

o z m b i e
    ^   ^        
Are these the letters you wish to swap? (y/n): y

The new word is: o z i b m e

Want to keep rearranging? (y/n): n

Word #2 is mummy
1: m
2: u
3: m
4: m
5: y

Enter the position numbers of the two letters you wish to swap:  etc...

A complete Example:

This example assumes an input file named words.txt with the following content - however, the user should be able to enter any file name and the file can contain any number of words:

Spring
Summer
Fall
Winter

Output of running Anagram.java

Welcome to the Anagram Arranger!

Please enter the name of your input file: abc.txt

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file: 123.txt

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file: words.txt

Word #1 is Spring
1: S
2: p
3: r
4: i
5: n
6: g

Enter the position numbers of the two letters you wish to swap: 3 5

S p r i n g
    ^   ^       
Are these the letters you wish to swap? (y/n): y

The new word is: S p n i r g

Want to keep rearranging? (y/n): yes

1: S
2: p
3: n
4: i
5: r
6: g

Enter the position numbers of the two letters you wish to swap: 1 6

S p n i r g
^         ^         
Are these the letters you wish to swap? (y/n): yes

The new word is: g p n i r S

Want to keep rearranging? (y/n): n

Word #2 is Summer
1: S
2: u
3: m
4: m
5: e
6: r

Enter the position numbers of the two letters you wish to swap: 2 3

S u m m e r
^ ^   
Are these the letters you wish to swap? (y/n): Yes

The new word is: S m u m e r

Want to keep rearranging? (y/n): Yes

1: S
2: m
3: u
4: m
5: e
6: r

Enter the position numbers of the two letters you wish to swap: 4 5

S m u m e r
      ^ ^       
Are these the letters you wish to swap? (y/n): y

The new word is: S m u e m r

Want to keep rearranging? (y/n): n

Word #3 is Fall
1: F
2: a
3: l
4: l

Enter the position numbers of the two letters you wish to swap: 1 2

F a l l
^ ^
Are these the letters you wish to swap? (y/n): y

The new word is: a F l l

Want to keep rearranging? (y/n): n

Word #4 is Winter
1: W
2: i
3: n
4: t
5: e
6: r

Enter the position numbers of the two letters you wish to swap: 1 3

W i n t e r
^   ^   
Are these the letters you wish to swap? (y/n): n
1: W
2: i
3: n
4: t
5: e
6: r

Enter the position numbers of the two letters you wish to swap: 1 4

W i n t e r
^     ^     
Are these the letters you wish to swap? (y/n): y

The new word is: t i n W e r

Want to keep rearranging? (y/n): y

1: t
2: i
3: n
4: W
5: e
6: r

Enter the position numbers of the two letters you wish to swap: 2 5

t i n W e r
^     ^       
Are these the letters you wish to swap? (y/n): y

The new word is: t e n W i r

Want to keep rearranging? (y/n): y

1: t
2: e
3: n
4: W
5: i
6: r

Enter the position numbers of the two letters you wish to swap: 3 4

t e n W i r
    ^ ^     
Are these the letters you wish to swap? (y/n): y

The new word is: t e W n i r

Want to keep rearranging? (y/n): n

Bye!

Corresponding output.txt for above example:

g p n i r S
S m u e m r
a F l l
t e W n i r

Required Error Checking

• Your Anagram.java should also do error checking for the following cases only:

1. The user inputs a position number that is higher than the position of the last character in the word
2. The user reverses the order of the two positions by giving the higher number followed by the lower number
3. The user enters the same position number twice.

• For the above errors, the program should print the message Invalid entry! and allow the user to try again, as shown in the example below.
• Additionally, the program should correctly handle the below error:

1. The user enters an incorrect name for a file.
   1. Error checking should be completed using a loop to handle multiple invalid inputs
   2. Error message must be:

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file:

• Please see below for examples of how to handle invalid input.

Error Checking Example:

Welcome to the Anagram Arranger!

Please enter the name of your input file: ddd.txt

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file: nnn.txt

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file: splooky.txt

Sorry. I cannot find a file by that name!
Please enter the name of a valid input file: spooky.txt

Word #1 is zombie
1: z
2: o
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 4 2

Invalid entry!

1: z
2: o
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 1 10

Invalid entry!

1: z
2: o
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 2 2

Invalid entry!

1: z
2: o
3: m
4: b
5: i
6: e

Enter the position numbers of the two letters you wish to swap: 2 3

z o m b i e
^ ^    
Are these the letters you wish to swap? (y/n): yes

The new word is: z m o b i e

Want to keep rearranging? (y/n): etc.