A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 99% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.

Rating (last year) 62 67 82 84 94 53 64 49 52 80

Rating (this year) 53 89 85 91 66 71 49 45 44 50

Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 99% confidence interval. Round your answers to one decimal place.

betting theory on tennis

A bookmaker has quoted odds on a tennis match between players I and II. The match consists of the best two out of three sets, i.e., if a player wins the first two sets, the third set is not played and the bet on it is canceled. The bookmaker is giving odds of 5 to 2 that player I will win the match and odds of 3 to 2 that player I will win each set. A bettor has 100 dollars which he can distribute by betting on either player I or II to win the match and any of the sets. All bets are made before the match starts (if there are only two sets, all bets on the third set are returned to the bettor).
(a) Find a way of placing bets so that no matter what happens the bettor is assured of winning an amount z where z is as large as possible. Formulate this problem as a linear programming and solve it using AMPL.
(b) What if now we have best three out of five sets, i.e., once a player wins three sets, no more sets are played and their corresponding bets are canceled, and everything else keeps the same? Re-solve the problem and compare the answer with part (a).

The Dilbert Investment Group employs 100 brokers. Twenty have been there less than 4 years, 50 have been there 4-8 years, and the rest have been there more than 8 years. A survey was distributed which asked brokers if they were Well Compensated, Fairly Compensated, or Poorly Compensated. Of the 20 brokers that were there less than four years; 8 said Well Compensated, 7 said Fairly Compensated and 5 said Poorly Compensated. Of the 50 there 4-8 years; the responses were 18, 20 and 12 respectively. Those there more than 8 years had responses of 8, 12 and 10 respectively.

a.) Develop a contingency table for the data.

b.) Find the probability that two brokers selected at random were both there less than 4 years.

c.) Find the probability that a broker said Fairly Compensated if there more than 8 years.

d.) Find the probability that a randomly selected broker said Well Compensated.

Estimation and Hypothesis Test (1 sample)

As an employee of a Retail Store and a recent graduate of the Accounting Program, you are responsible for an advertising campaign aimed at increasing the amount spent by customers.

After the advertising campaign, a random sample of 50 customers and the amount spent at the store was recorded as follows:

Amount spent:                          $150, 122, 210, 183, 50, 423, 158, 281, 190, 260,

                                                   180, 125, 210, 188, 224, 253, 320, 243, 180, 363,

                                                   220, 180, 240, 230, 180, 200, 460, 130, 72, 165

                                                   130, 252, 44, 134, 467, 412, 188, 352, 189, 318

                                                   120, 220, 240, 245, 80, 225, 268, 108, 220, 480

1. What is the best estimate of the average amount a buying customer spent at the store after the advertising campaign?

2. Determine the 90% confidence interval for the average amount spent at the store after the advertising campaign. Interpret its meaning.

3. Before the advertising campaign, the average amount spent at the store is $ 175.

Perform a hypothesis test to determine if there is sufficient evidence that the advertising campaign didn’t change the average amount a customer spent at the store. Test at 2% significance level. (Include null and alternative Hypothesis, test statistics, critical value, reject region, and conclusion

Dealing Cards

Write a program that deals a deck of card into 4 hands – Each hand having 13 cards.

• Your program should do the followings
  • use an array to randomly select 52 cards and deal it into 4 hands.
  • Print each hand unsorted
  • Identify the face value of each hand and display it.
  • You should create a class called Card, and all the methods should be defined within the card class.

Hints – Import below java utility to use the random function.

import java.util.*;

Random rand = new Random();

int r = rand.nextInt(52); // this will generate random numbers between 0-52

to get a value between 1-13, use the mod function and get the remainder

if your number is 15, 15%13 has a remainder of 2. 2 is your face card.

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11 = jack

12= Queen

13= King

Card is a CLUB - If your generated number is between (1-13)

Card is a Diamond - If your generated number is between (14-26)

Card is a Spade - If your generated number is between (27-39)

Card is a Heart - If your generated number is between (40-52)

Your program output should look like this below

----------------------------------------------------------------------------------------------------------------------------------

Deck of cards shuffled into 4 hands

8 1 7 18 43 26 31 2 12 3 40 22 4

29 9 10 11 5 35 47 36 25 14 17 39 23

21 52 6 46 38 48 24 16 27 32 13 45 42

49 44 50 20 37 34 51 15 28 30 19 33 41

Face of cards in each Hand

Hand 1:

       Clubs: 8 1 7 2 Q 3 4

       Diamonds: 5 K 9

       Spades: 5

       Heart: 4 1

Hand 2:

       Clubs: 4 9 10 J 5

       Diamonds: Q 1 4

       Spades: 3 9 10 K

       Heart: 8

Hand 3:

       Clubs: 6 K

       Diamonds: 10 8 J 3

       Spades: K Q 1 6

       Heart: K 7 9

Hand 4:

       Clubs: K

       Diamonds: 7 2

       Spades: J 8 2 4

Heart: 6 3 10 5 J Q

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

Step 1:
Choose four numbers that have the smallest possible standard deviation. What is the numerical value of s in this case? Give your answer as a whole number (meaning no decimal places).

Step 2:
Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation?

1. Indicate the status of each of the listed ledger accounts.

2. The following are the steps in the financial accounts compilation, using a spread sheet approach. List the steps in the correct order in which they are to be completed, given the list of ledger accounts at fiscal year-end: (Simply match the letter with the number in the box).
a. Prepare adjusted trial balance                                             f. Post transactions
b. Prepare an unadjusted trial balance                                    g. Journalize transactions

2. The following are the steps in the financial accounts compilation, using a spread sheet approach. List the steps in the correct order in which they are to be completed, given the list of ledger accounts at fiscal year-end:

(Simply match the letter with the number in the box).
a. Prepare adjusted trial balance                                             f. Post transactions
b. Prepare an unadjusted trial balance                                    g. Journalize transactions
c. Prepare the income summary.                                            h. Close the temporary accounts
d. Adjust the ledger accounts                                                  j. Prepare a post-closing trial balance
e. Analyze transactions

4. At the beginning of 2018, Beta Company's balance sheet reported Total Assets of $255,000 and Total Liabilities of $124,000. During 2018, the company reported total revenues of $275,000 and expenses of $187,000. Also, owner withdrawals during 2018 totaled $35,000. Assuming the owner contributed an additional $15,000 during the year, what will be the balance in the owner's capital account at the end of 2018?

5. On 10/15/2019, a company borrowed $28,000 from a bank, for 90 days, at 6% interest. Payment of capital and interest is on due date. On fiscal year end 12/31/2019, the company needed to record interest owed. Record the adjusting entry necessary.

6. The following unadjusted and adjusted trial balances were taken from the current year's accounting system for High Point, Inc.

In general journal form, present the six adjusting entries that explain the changes in the account balances from the unadjusted to the adjusted trial balance.

7. A company purchased $6,800 worth of merchandise 3/10, N/35. Transportation cost was an additional $65, paid in cash. Three days after receipt of merchandise, the company returned $300 worth of merchandise. It later paid the invoice within eight days of purchase. The total cost of this merchandise taken into inventory, under the perpetual inventory system, will be what amount?

8. A company markets a sports equipment and uses the perpetual inventory system to account for its merchandise. The beginning balance of the inventory and its transactions during the first week of January, football cleats were as follows:
January 1           Beginning balance          20 pairs @ $35 per pair.

January 3           Purchased                        36 pairs @ $38 per pair.

January 4           Sold                                 25 pairs @ $50 per pair.

January 6           Purchased                        22 pairs @ $40 per pair.

January 7           Sold                                 30 pairs @ $50 per pair.

Required: Using the LIFO method of valuation, determine the:   a) Cost of sales

                                                                                                                           b) Value of the ending inventory.

c. Prepare the income summary.                                            h. Close the temporary accounts
d. Adjust the ledger accounts                                                  j. Prepare a post-closing trial balance
e. Analyze transactions

9. Neighborhood Electronics runs a small store carrying four items of inventory. At the end of its fiscal year, the physical stock take, their book value, and the market (replacement) price was compiled.

                                                       Units                  Book cost       Market price

              Cell phones                     128                     $85                             $66

              Android Tablets                76                         54                                 60

              Kindles                              47                     105                               108  

              Chrome books                24                         63                                 61    

The company's policy is to record closing inventory at lower of cost or market value, using individual valuation. What correcting entries will this company make at the fiscal year end? (Use the below journal template).

                                                                                   Adjustment Journal

10. Fill in the numbered spaces 1 - 9, in the following separate income statements, for non-related companies A through C.

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Give state diagram of DFA recognizing L={w | w is 0,1-string, and contains 3k 0s and 2m 1s for some integers k and m at least 0}. For examples, 0010111 is in L, but 010011 is not in L. The first string contains 3 0s and 4=2x2 1s, but the second string has an odd number of 1s.

Compute the cost of not taking the following trade discounts: (Use 365 days in a year. Round the intermediate calculations to 4 decimal places. Round the final answer to 2 decimal places.)

a. 2/13, net 50.

Cost of lost discount             %

b. 2/20, net 50.

Cost of lost discount              %

c. 3/18, net 65.

Cost of lost discount             %

d. 3/18, net 150.

Cost of lost discount             %