1. For the given data set representing the runs scored by two players in last 15 matches, conduct the following analysis:

i. Which average you will use to summarize the performance of the player? Find average runs scored for both of the players. Also give reasons for the choice of the average?

ii. If selection is possible on the basis of consistency, which player would you choose in the team? Perform the required statistics and justify the selection.

iii. Check whether there exists any relationship among the runs scored by two players using Karl Pearson coefficient of correlation and interpret the same.

The following tables list the numbers of home runs hit by the leaders in the National and American Leagues. (A graphing calculator is recommended.) Home Run Leaders National League 70 42 72 35 52 64 45 55 46 63 59 61 63 62 35 66 36 62 36 54 71 31 33 54 58 65 69 52 35 62 71 38 58 52 American League 57 44 41 57 38 56 42 41 50 56 41 23 54 40 53 28 53 27 22 38 48 40 25 35 39 38 40 44 42 41 29 30 30 31 (a) Find the mean and the population standard deviation of the number of home runs hit by the leaders in the National League. Round each result to the nearest tenth. mean home runs population standard deviation home runs (b) Find the mean and the population standard deviation of the number of home runs hit by the leaders in the American League. Round each result to the nearest tenth. mean home runs population standard deviation home runs (c) Which of the two data sets has the larger mean? National League American League Which of the two data sets has the larger standard deviation? National League American League

This assignment will acquaint you with the use of while loops and boolean expressions. You will create a program that acts as a score keeper of a racquet ball game between two players. The program will continually ask the user who the winner of every point is as the game is played. It will maintain the scores and declare the match is over, using these rules: (1) A game is over when a. one of the players wins 7 points or, b. one of the players wins 3 points while the other player has 0 points. (2) The match is over when one of the players wins 2 games. The program will run a single match. See sample runs below. Write a complete class called RacquetBallMatch that has the following: • (8 points) playGame method: that plays one full game of 7 points between two players Allen and Bob. This method accepts a Scanner object and returns the name of the winner of this game. Specifically, this method repeatedly asks the user “who the winner of the next point is” until the game is over by following the rules mentioned above. The user is expected to enter the first letter of the player’s names, i.e. A for Allen and B for Bob. (Make the input case insensitive) See sample runs below. • (2 points) printGameScores method: accepts points of two players and prints the scores. See sample runs below. • (2 points) printMatchScores method: accepts game counts of two players and prints the scores. See sample runs below. • (5 points) main method: o Welcomes the user. o Declares and initializes a Scanner object to be used throughout to read user input. o Calls the playGame method repeatedly until the winner of a 3-game set can be declared. For example, if Bob wins the first 2 games, he would be declared the match winner and the program would stop. • (3 points) Include appropriate program documentation and formatting including: Your first and last name, the date of submission, code comments necessary to explain the operation of your program, and proper indentation of the code, etc. Notes: • For each of the methods, think about the following: What is the return type, what parameter(s) will it need to perform the task, and accordingly decide the method signature for each. • Don’t use static variables (variables that are declared outside of all the methods). It is ok to have class constants (variables declared with final keyword). • Use while-loops to handle the repetition. • Make sure there is no code-duplication. • Use a Boolean variable that captures the winning condition for a game or the match and use it in the while-loop conditions.

1. Suppose that two integers from the set of 8 integers {1, 2, … , 8} are choosen at random. Find the probability that

1. 5 and 8 are picked.

2. Both numbers match.
3. Sum of the two numbers picked is less than 4.

2. [3+3+4 marks] Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that:

1. The bit string has the sum of its digits equal to seven.
2. The bit string has more 0s than 1s.

The bit string has exactly two 1s, given that the string begins with a 1

Run Length Encoding

It is sometimes important to minimise the space used for storing data. This idea of data compression can be implemented in many forms. One of the simpler techniques is known as Run Length Encoding (RLE). RLE takes advantage of the fact that in many cases, data will contain a run of repeated 0s or 1s, and these runs can be represented by a shorter code. RLE is a technique used in some image or sound formats to reduce the overall size of the file. There are many variations of this process, but for this assignment, you will use the 3-bit encoding version described below.

1. Given binary data represented by a sequence of 0s and 1s, break the number into runs of 0s and 1s and note the length of each run.
2. For any run of more than 7, break the run into groups of 7 or smaller.
3. For each run, create an encoded form by first placing the type of run 0 or 1 and then the binary representation of the run’s length.
4. Write out the encoded form of data by taking each encoded run and separating them with spaces. Be sure to keep the original order of the data intact.

Example:

Given 11111000000010000001111111000000, what is the RLE form of this data?

Breaking this into runs gives us 5 1s, 7 0s, 1 1s, 6 0s, 7 1s, 6 0s

For each group, combine the type of run followed by the length in binary. Use spaces to separate each run:

1101 0111 1001 0110 1111 0110 is the RLE form.

Data Compression

Data compression is the ratio of the compressed data over the uncompressed data. In this case, the compressed data is 24 bits (including the spaces, which must be counted), and the original data is 32 bits. This gives a data compression ratio of 0.75.

Question 1a: What is the RLE of the following?

1111100000000000

Question 1b:

What is the compression ratio for the answer to Question 1a?

Question 2a: What is the RLE of the following?

101010

Question 2b:

What is the compression ratio for the answer to Question 2a?

Could you please help with these questions with enough explanation?

Thanks a lot

For a sports radio talk show, you are asked to research the question whether more home runs are hit by players in the National League or by players in the American League. You decide to use the home run leaders from each league for the last 40 years as your data.

National League

47        49        73        50        65        70        49        47        40        43

46        35        38        40        47        39        49        37        37        36

40        37        31        48        48        45        52        38        38        36

44        40        48        45        45        36        39        44        52        47

American League

47        57        52        47        48        56        56        52        50        40

46        43        44        51        36        42        49        49        40        43

39        39        22        41        45        46        39        32        36        32

32        32        37        33        44        49        44        44        49        32

What are you hypotheses?

The significance level is α = 0.05

1 : An array a is defined to be self-referential if for i=0 to a.length-1, a[i] is the count of the number of times that the value i appears in the array. As the following table indicates, {1, 2, 1, 0} is a self-referential array.

Here are some examples of arrays that are not self-referential:

{2, 0, 0} is not a self-referential array. There are two 0s and no 1s. But unfortunately there is a 2 which contradicts a[2] = 0.

{0} is not a self-referential array because there is one 0, but since a[0] = 0, there has to be no 0s.

{1} is not a self-referential array because there is not a 0 in the array as required by a[0] = 1.

Self-referential arrays are rare. Here are the self-referential arrays for arrays of lengths up to 10 elements:

{1, 2, 1, 0} (see above)
{2, 0, 2, 0} (there are two 0s, no 1s, two 2s and no 3s
{2, 1, 2, 0, 0}  (there are two 0s, one 1, two 2s, no 3s and no 4s)
{3, 2, 1, 1, 0, 0, 0} (there are three 0s, two 1s, one 2, one 3, no 4s, 5s or 6s)
{4, 2, 1, 0, 1, 0, 0, 0} (there are four 0s, two 1s, one 2, no 3s, one 4, and no 5s, 6s, or 7s)
{5, 2, 1, 0, 0, 1, 0, 0, 0} (there are five 0s, two 1s, one 2, no 3s or 4s, one 5, and no 6s, 7s, or 8s)
{6, 2, 1, 0, 0, 0, 1, 0, 0, 0} (there are six 0s, two 1s, one 2, no 3s, 4s, or 5s, one 6, and no 7s, 8s, or 9s)

Write a function named isSelfReferential that returns 1 if its array argument is self-referential, otherwise it returns 0.

If you are programming in Java or C#, the function signature is
   int isSelfReferential(int[ ] a)

If you are programming in C or C++, the function signature is
   int isSelfReferential(int a[ ], int len) where len is the number of elements in the array

A woman runs 50 meters at 54 degrees north of east. She then runs 40 meters at 47 degrees north of east. She then runs 34 meters south of east at 30 degrees. What would her displacement be? Draw, explain, and show your work.

Data Set

1.Use the data sheet and enter data from 1-15 as Group A for the variable height and from 16-30 as Group B for the variable height in an Excel program.

2.Assuming equal variances, conduct a two-tailed, independent t-test on the data.

3.Next, conduct a two-tailed, dependent t-test on the data (no need to assume equality of variance in a dependent t-test).

4.Complete the seven-step process for each of the t-tests in this documents.

5.Answer all three parts o this assignment, including the writen portion at the end.

Part 1: Seven-Step Process for the Two-Tailed Test of Independent Samples

Step 1: Set your hypothesis.

Ho: (in statistical form)

Ha: (in statistical form)

Step 2: Determine testing Alpha Level – Alpha level = ___

Step 3: Sampling distribution = t?

Step 4: Decision Rule—I will reject the Ho if my tobs value falls at or beyond my tcrit value of ______; otherwise, I will fail to reject.

Step 5: Calculate P-value in excel P-value = ______

Step 6: Since my P-value of ______ is (< or >--choose symbol) than my chosen Alpha Level of _____, I, therefore, reject or fail to reject (choose one) the null hypothesis.

Step 7: Since I rejected or failed to reject (choose one) the null hypothesis, I, therefore, conclude (fill in the conclusion based on your decision in step 6).

Part 2: Seven-Step Process for the Two-Tailed Test of Dependent Samples

Step 1: Set your hypothesis.

Ho: (in statistical form)

Ha: (in statistical form)

Step 2: Determine testing Alpha Level – Alpha level = ___

Step 3: Sampling distribution = t?

Step 4: Decision Rule—I will reject the Ho if my tobs value falls at or beyond my tcrit value of ______; otherwise, I will fail to reject.

Step 5: Calculate P-value in excel P-value = ______

Step 6: Since my P-value of ______ is (< or >--choose symbol) than my chosen Alpha Level of _____, I, therefore, reject or fail to reject (choose one) the null hypothesis

Step 7: Since I rejected or failed to reject (choose one) the null hypothesis, I, therefore, conclude (fill in the conclusion based on your decision in step 6).

Part 3: Contrasting the Independent and Dependent Tests

In a brief paragraph, discuss your reasoning for any differences between the two tests in the seven-step process.

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 12 randomly selected games are shown below. Attendance 18 27 24 30 22 17 30 43 53 38 47 27 Runs 4 4 9 10 5 7 8 11 9 12 8 5 Find the correlation coefficient: r = Round to 2 decimal places. The null and alternative hypotheses for correlation are: H 0 : = 0 H 1 : ≠ 0 The p-value is: (Round to four decimal places) Use a level of significance of α = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance. There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance. There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful. r 2 = (Round to two decimal places) (Round to two decimal places) Interpret r 2 : Given any fixed attendance, 34% of all of those games will have the predicted number of runs scored. There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 34%. 34% of all games will have the average number of runs scored. There is a 34% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game. The equation of the linear regression line is: ˆ y = + x (Please show your answers to two decimal places) Use the model to predict the runs scored at a game that has an attendance of 26,000 people. Runs scored = (Please round your answer to the nearest whole number.) Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. The slope has no practical meaning since the total number runs scored in a game must be positive. For every additional thousand people who attend a game, there tends to be an average increase of 0.14 runs scored. Interpret the y-intercept in the context of the question: The average runs scored is predicted to be 3. The best prediction for a game with 0 attendance is that there will be 3 runs scored. If the attendance of a baseball game is 0, then 3 runs will be scored. The y-intercept has no practical meaning for this study.