The following data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Earned Run Average, or ERA. The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - Y, and its Earned Run Average (ERA) - X. Winning Proportion - Y Earned Run Average (ERA) - X 0.623457 3.13 0.512346 3.97 0.635802 3.68 0.604938 3.92 0.518519 4.00 0.580247 4.12 0.413580 4.29 0.407407 4.62 0.462963 3.89 0.450617 5.20 0.487654 4.36 0.456790 4.91 0.574047 3.75 (a) Using MINITAB, create a scatter-plot of the data. What can you conclude from this scatter-plot? A. There is not a linear relationship between the a teams winning percentage and its ERA. B. There is a positive linear relationship between a teams winning percentage and its ERA. C. There is a negative linear relationship between a teams winning percentage and its ERA. (b) Use MINITAB to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers. Yˆi = Xi (c) Find the value of the coefficient of determination, then complete its interpretation. r2= (use four decimals) The percentage of in that is explained by its linear relationship with is equation editorEquation Editor %. (d) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data. As a teams increases by the teams will equation editorEquation Editor . (use four decimals) (e) A certain professional baseball team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win? Use two decimals in your answer. games won (f) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer. ei=

The following data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Earned Run Average, or ERA.

The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - YY, and its Earned Run Average (ERA) - XX.

(a) Using R-Studio, create a scatter-plot of the data. What can you conclude from this scatter-plot?

A. There is a negative linear relationship between a teams winning percentage and its ERA.
B. There is a positive linear relationship between a teams winning percentage and its ERA.
C. There is not a linear relationship between the a teams winning percentage and its ERA.


(b) Use R-Studio to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers.

YˆiY^i =

equation editor

  ? + -  

equation editor

XiXi

(c) Find the value of the coefficient of determination, then complete its interpretation.

r2=r2=

equation editor

(use four decimals)

The percentage of  ? variation standard deviation the mean  in  ? a teams winning percentage a teams earned run average  that is explained by its linear relationship with  ? the teams winning percentage the teams earned run average  is

equation editor

%.

(d) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data.

As a teams  ? winning percentage earned run average  increases by  ? one percentage point one earned run  the teams  ? winning percentage earned run average  will  ? will increase by an average of will decrease by an average of will increase by will decrease by  

equation editor

. (use four decimals)

(e) A certain professional baseball team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win? Use two decimals in your answer.

equation editor

games won

(f) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer.

I need to write a function that counts the number of total wins and losses.

I have a text file called analysis_data.txt with 1000 lines written

Won

Loss

Won

Loss

Won

Won

...

The function need to do the following:

Opens the analysis_data.txt file and reads through all the data, counting number of 'Won' and 'Loss' words stored in the file. Returns two integers: count of wins and count of losses from the text file.

**Can't use the break statement

A woman stands on a scale in a moving elevator. Her mass is 61.0 kg, and the combined mass of the elevator and scale is an additional 725 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9340 N. What does the scale read (in N) during the acceleration?

You are an engineering consultant hired to verify an elevator design. The elevator mass is 500kg and has a maximum occupant capacity of 800kg. Carbon steel cables with total cross sectional area of 64cm2 support the elevator. The maximum speed of the elevator is 2 meters per second. At the maximum speed, each cable extends at least 4 meters and cannot extend more than 22 meters, unstretched. When the car is not moving and the cables are extended by 22 meters of (unstretched) cable, there is 3 meters of clearance between the bottom of the elevator and the concrete floor of the shaft.

Carbon Steel Cable:

Young’s Modulus: 207 GPa

Yield Strength:      131 MPa

Ultimate Strength: 290 Mpa

Requirements for the elevator include a factor of safety of 3 for cable failure and the occupants must not ever experience more than 5 times the acceleration of gravity.

Make a sketch of the problem.

Answer the following questions:

1.If the elevator is moving at maximum speed and the motor suddenly stops, what is the worst case for cable failure?

2.What is the value of the worst case stress in the cable (MPa)?

3.The design meets the cable failure factor of safety requirement. (T/F)

4.If the elevator is moving at maximum speed and the motor suddenly stops, what is the worst case for occupant acceleration?

5.Describe at least one change to improve the design. Explain how your suggestion would improve performance relative to the requirements.

Consider the finite state machine shown below that controls a two story elevator. The elevator has a toggle button that can be in the UP position or the DOWN position, and an LED light that can be RED or GREEN . When the elevator is on the GROUND floor the light is RED, and when the elevator is on the FIRST floor the light is GREEN.

Assume the existence of function

enum Button getButton();

that returns a value of DOWN or UP, given enumeration

enum Button {DOWN, UP};

Note the function getButton() already exists so you do not need to define this function, you just need to call this function.

First, define two additional enumerations named State and LED to represent the values GROUND and FIRST, and RED and GREEN, respectively.

Second, write an infinite while loop that first sets the value of a variable that represents the color of the led to either RED or GREEN according to which floor the elevator is currently stationed. Then call function getButton() to read the current position of the toggle button and reassign the value of a variable to represent the next desired floor state of the elevator to either GROUND or FIRST. Assign the elevator to initially reside on the GROUND floor, and assume the elevator moves infinitely fast and will move to the desired floor immediately when the floor state variable is reassigned.

Only show the enumerations and while loop code. Do not define any functions or an entire program with a main function.

in c

In C code Consider the finite state machine shown below that controls a two story elevator. The elevator has a toggle button that can be in the UP position or the DOWN position, and an LED light that can be RED or GREEN . When the elevator is on the GROUND floor the light is RED, and when the elevator is on the FIRST floor the light is GREEN.

Assume the existence of function

enum Button getButton();

that returns a value of DOWN or UP, given enumeration

enum Button {DOWN, UP};

Note the function getButton() already exists so you do not need to define this function, you just need to call this function.

First, define two additional enumerations named State and LED to represent the values GROUND and FIRST, and RED and GREEN, respectively.

Second, write an infinite while loop that first sets the value of a variable that represents the color of the led to either RED or GREEN according to which floor the elevator is currently stationed. Then call function getButton() to read the current position of the toggle button and reassign the value of a variable to represent the next desired floor state of the elevator to either GROUND or FIRST. Assign the elevator to initially reside on the GROUND floor, and assume the elevator moves infinitely fast and will move to the desired floor immediately when the floor state variable is reassigned.

Only show the enumerations and while loop code. Do not define any functions or an entire program with a main function.

Home vs Road Wins – Significance Test: For the NHL regular season, the Chicago Blackhawks won 26 out of 41 home games and won 18 out of 41 away games. Clearly the Blackhawks won a greater proportion of home games. Here we investigate whether or not they did significantly better at home than on the road. The table summarizes the relevant data. The p̂'s are actually population proportions but you should treat them as sample proportions. The standard error (SE) is given to save calculation time if you are not using software.

Data Summary

SE = 0.11014

The Test: Test the claim that the proportion of wins at home was significantly greater than on the road. Use a 0.01 significance level.

(a) Letting p̂₁ be the proportion of wins at home and p̂₂ be the proportion of wins on the road, calculate the test statistic using software or the formulaz =

where δ_p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) given with the data.  Round your answer to 2 decimal places.
z =  
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software or the z-table to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(c) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(d) Choose the appropriate concluding statement.

The data supports the claim that the proportion of wins at home was significantly greater than on the road.While the proportion of wins at home was greater than on the road, the difference was not great enough to be considered significant.       We have proven that the Blackhawks always do better at home games. We have proven there was no difference in the proportion of wins at home than wins on the road.

Home vs Road Wins – Significance Test: For the NHL regular season, the Chicago Blackhawks won 27 out of 41 home games and won 18 out of 41 away games. Clearly the Blackhawks won a greater proportion of home games. Here we investigate whether or not they did significantly better at home than on the road. The table summarizes the relevant data. The p̂'s are actually population proportions but you should treat them as sample proportions. The standard error (SE) is given to save calculation time if you are not using software.

Data Summary

SE = 0.10990

The Test: Test the claim that the proportion of wins at home was significantly greater than on the road. Use a 0.05 significance level.

(a) Letting p̂₁ be the proportion of wins at home and p̂₂ be the proportion of wins on the road, calculate the test statistic using software or the formulaz =

where δ_p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) given with the data. Round your answer to 2 decimal places.
z =
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software or the z-table to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(c) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(d) Choose the appropriate concluding statement.

The data supports the claim that the proportion of wins at home was significantly greater than on the road.

While the proportion of wins at home was greater than on the road, the difference was not great enough to be considered significant.    

We have proven that the Blackhawks always do better at home games.

We have proven there was no difference in the proportion of wins at home than wins on the road.

A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 181 lb and a standard deviation or 32 lb. You need to design an elevator that will safely carry 12 people. Assuming a worst case scenario of 12 male passengers, find the maximum total allowable weight if we want to a 0.999 probability that this maximum will not be exceeded when 12 males are randomly selected.

maximum weight = -lb

Enter your answer rounded to the nearest whole number. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.