In​ baseball, League A allows a designated hitter​ (DH) to bat for the​ pitcher, who is typically a weak hitter. In League​ B, the pitcher must bat. The common belief is that this results in League A teams scoring more runs. In interleague​ play, when League A teams visit League B​ teams, the League A pitcher must bat.​ So, if the DH does result in more​ runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this​ claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Complete parts​ a) through​ d) below.

a) Draw​ side-by-side boxplots of the number of runs scored by League A teams with and without their DH. Choose the correct graph below.

A.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 13. An x is plotted at 14. The top boxplot is labeled B and has vertical line segments at 3, 4.5, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 11.

B.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 9. Three x's are plotted at 12, 13, and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 10.

C.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 3, 5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12. Two x's are plotted at 13 and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12.

D.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 1 and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12.

Does there appear to be a difference in the number of runs between these​ situations?

A. No but the number of runs scored in a League A park appear to be slightly higher than the number of runs scored in a League B park.

B. Yes because the number of runs scored in a League B park appear to have a higher median than the number of runs scored in a League A park.

C.Yes because the number of runs scored in a League A park appear to have a higher median than the number of runs scored in a League B park.

D.No because the number of runs scored in a League A park is about the same as the number of runs scored in a League B park.

​b) Explain why a hypothesis test may be used to test whether the mean number of runs scored for the two types of ballparks differ.

Select all that apply.

A.Each sample has the same sample size.

B.Each sample is obtained independently of the other.

C.Each sample size is small relative to the size of its population.

D.Each sample is a simple random sample.

E.Each sample size is large.

​c) Test whether the mean number of runs scored in a League A park is greater than the mean number of runs scored in a League B park at the

alphaα=0.05 level of significance.

Determine the null and alternative hypotheses for this test. Let mu Subscript Upper AμA

represent the mean number of runs scored by a League A team in a League A park and let

mu Subscript Upper BμB represent the mean number of runs scored by a League A team in a League B park.

Upper H 0H0​:

▼

sigma Subscript Upper AσA

pp mu Subscript Upper AμA

▼

greater than>

equals=

less than<

not equals≠

▼

sigma Subscript Upper BσB

mu Subscript Upper BμB

p 0p0

versus

Upper H 1H1​:

▼

mu Subscript Upper AμA

pp

sigma Subscript Upper AσA

▼

greater than>

equals=

less than<

not equals≠

▼

p0 mu Subscript Upper BμB sigma Subscript Upper BσB Find t0​,the test statistic for this hypothesis test. t0=nothing

​(Round to two decimal places as​ needed.)

Determine the​ P-value for this test.

​P-value=

​(Round to three decimal places as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

A.Do not reject Upper H0. There is not sufficient evidenceThere is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

B.Reject Upper H 0H0.There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

C.Do not reject Upper H0.There is sufficient evidenceat the level of significance to conclude that games played with a designated hitter result in more runs.

D.Reject Upper H0. There is sufficient evidenceThere is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

​d) Construct a 95​% confidence interval for the mean difference in the number of runs scored by League A teams in a League A park and the number of runs scored by League A teams in a League B park. Interpret the interval.

Lower​ bound:

Upper​ bound:

​(Round to three decimal places as​ needed.)

Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Round to three decimal places as needed. Use ascending​ order)

A. We are 95​%confident the difference between the mean number of runs scored in a League A park and the mean number of runs scored in a League B park is between nothing and nothing.The confidence interval does not containdoes not contain ​zero, so there is sufficient evidence to conclude there is a difference in the mean number of runs scored with or without the DH.

B. We are 95​% confident the difference between the mean number of runs scored in a League A park and the mean number of runs scored in a League B park is between nothing and nothing.The confidence interval contains ​zero, so there is notis not sufficient evidence to conclude there is a difference in the mean number of runs scored with or without the DH.

Task: Craps is a popular game played in casinos. Design a program using Raptor Flowcharts to play a variation of the game, as follows:

Roll two dice. Each dice has six faces representing values 1, 2, 3, 4, 5, and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12(called craps), you loose; if the sum is 7 or 11(called natural), you win; if the sum is another value(i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue roll the dice again, if the same point value is rolled, you win, otherwise, you loose. Please use Raptor Flowcharts to make the program

Your program should allow user play as many runs as wanted and display each run status and result. And display total number of runs user played and number of runs user won.

Here is a sample output:

Run 1:

You rolled 5 + 6 = 11

You Win!!!

Run 2:

You rolled 1 + 3 = 4

Point is 4, you have another try to win this run.

Rolled Again 2 + 4 = 6

You loose

Run 3:

You rolled 4 + 4 = 8

Point is 8, you have another try to win this run.

Rolled Again 2 + 6 = 8

You win!

Run 4:

You rolled 6 + 6 = 12

You loose

Total Runs: 4

User Won 2 of the 4 runs.

INSTRUCTIONS: Attempt ALL questions

There are 30 students in a class. Among them, 8 students are learning both Audit and Tax. A total of 18 students are learning Audit. If every student is learning at least one language, how many students are learning Tax in total?

Among a group of students, 50 played cricket, 50 played hockey and 40 played volley ball. 15 played both cricket and hockey, 20 played both hockey and volley ball, 15 played cricket and volley ball and 10 played all three. If every student played at least one game, find the number of students and how many played only cricket, only hockey and only volley ball?

QUESTION THREE

Measures of dispersion are often used in finance as a proxy for risk. Explain.

Data Set

Given the population mean for weight at 191.00 pounds, but no population standard deviation, using t = X-bar - µ/est. σx̄, and alpha .01, perfom the following seven-step process and contstruct the appropriate confidence intervals. Please write it out (fill-in the blanks) as detailed below.,

Step 1: Ho: u _ ____

               Ha : u _ ____

Step 2: Alpha level = ______

Step 3: Sampling distribution is ____________________

Step 4: Decision Rule—I will reject the Ho if the |_____| value falls at or beyond
the |_____| of _____, otherwise I will fail to reject

Step 5: Calculation—\_z_obs or t_obs__/ = ____

Step 6: Summary—Since the |____| of ____ falls at or beyond the |____| of ____, I therefore _________________.

Step 7: Conclusion—Since _________________ Ho occurred, I conclude that __________________________ in mean height value.

And the confidence intervals:

Please code in C# (C-Sharp)

Assignment Description

A pirate needs to do some accounting and has asked for your help. Write a program that will accept a

pirate’s starting amount of treasure in number of gold pieces. The program will then run one of two

simulations, indicated by the user:

1) The first simulation runs indefinitely, until one of two conditions is met: the pirate’s treasure

falls to 0 or below, or the pirate’s treasure grows to 1000 or above.

2) The second simulation runs for a number of years set by the user.

For both simulations, each year the pirate has an equal chance to either gain or lose 50 gold pieces. At

the end of each year, the pirate’s total gold and the year is displayed to the user. Validate all user input.

Tasks

1) The program needs to contain the following

a.

A comment header containing your name and a brief description of the program

b. At least 5 comments besides the comment header throughout your code

c.

A prompt for the starting treasure amount

d. A prompt to choose a simulation

i. The first simulation continues until the treasure amount becomes 1000 or more

or 0 or less

ii. The second simulation will prompt the user for number of years, then simulate

that many years. The gold amount can go below zero

e. For both simulations, treasure amount has an equal chance to increase by 50 or

decrease by 50 each year

f.

Output the year and treasure amount after each year

g.

“Press enter to continue” and Console.ReadLine(); at the end of your code

h. Validate all user input. Either through exception handling or boolean logic.

2) Upload a completed .cs file onto the Assignment 5 submission folder and a word document

containing the following six (6) screenshots:

a.

One run of the first simulation, starting amount 500

i. Your screenshot only needs to show up to the last 10 years

b. Two runs of the second simulation, starting amount 300 for 10 years and starting

amount 500 for 20 years

c.

Three test runs with invalid input for the following: starting treasure amount, simulation

choice, number of years

Explain the correlation coefficient of determination.

a. Height Vs. Weight with an alpha of 0.05/2

b. Weight vs age alfpha 0.01/2

c. Height vs shoe sz an alpha of =0.02/2

he manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Find a 99% confidence interval on the difference in the mean life.

A football player runs for a distance d1 = 8.55 m in 1.33 s, at an angle of θ = 62.1degrees to the 50-yard line, then turns left and runs a distance d2 = 10.68 m in 2.19 s, in a direction perpendicular to the 50-yard line. The diagram shows these two displacements relative to an xy coordinate system, where the x axis is parallel to the 50-yard line, and the y axis is perpendicular to the 50-yard line. What angle, in degrees, does the displacement make with the y axis? (Note that the angle θ was given as measured from the x axis rather than the y axis.)

An Ontario farmer owns two orchards, one near the lakeshore and one near the escarpment (a high cliff that runs south of Lake Ontario). He wants to find out if topography plays a role in the development of his apples. From the lakeshore orchard, he randomly collects 15 apples which have an average weight of 86g and a standard deviation of 7. From the escarpment orchard, he randomly collects 10 apples with an average weight of 80g and a standard deviation of 8. Is there a difference in the weight of the apples at both locations?