Perfect Properties have collected sales data from property sales in the northern suburbs of Cape Town for the past month. In the table below you are supplied with the selling price (SP) of the house in Rand, the size of the plot in m² (P) as well as the size of the house, also in m² (H). They are interested in understanding which of these two factors influence the selling price.

Use the data in the sheet named “Perfect” and answer the following questions:

1. Decide which linear regression model (with size of plot (P) or size of house (H) or both as independent variable) is the better model in explaining the behaviour of selling prices (SP) and motivate your selection.

The remaining answers must be based on the model that you have selected.

2. What is the total variation in “Selling Price” that is explained by the independent variable(s) that you have selected?
3. Is the overall regression model statistically significant? Test at the 5% level of significance using the model that you have selected in a. For this test formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
4. Write down the linear regression equation in algebraic format using SP for Selling price, P for plot size and H for the size of the house.
5. Compute the expected Selling price for a house that stands on a plot of 1500 m² and has a house that covers 245 m².

Compute the 95% confidence interval of the mean expense for a house that stands on a plot of 1500 m² and has a house that covers 245 m².

1.A 1000 ephemeral stream segment along the Town Creek near Tupelo, MS has a width of 30-m. The difference in elevation of the bottom channel for the upstream to the downstream section is 0.5m. A triangular hydrograph cumulating 10-cm of runoff that begins at 0m3/s reaches a peak of 35m3/s after the first hour of flow and returns to 0m3/s at the time 2.8-hr.If no lateral or overbank inflow is observed along the reach:

a.(15pts) Compute the outflow hydrograph for this reach selecting a time step of 0.1hr, a travel time constant of 0.285 hr and a weighting factor o f0.35.(use 4 decimal places for the outflow hydrograph to determine the routing time to reach the 0m3/s)(As you could submit your routingin Excel, hand/typing calculation are required for the time step that corresponds to your last digit of the net id. If 0 then 10th time step)Hint: The inflow hydrographs should have time steps of 0.1-hr from the beginning to the end.

b.(5 pts) Determine the lag time and peak flow attenuation(difference) observed between inflow and outflow hydrographs.

c.(15pts) Assuming the routing parameters remain constant, compute the outflow hydrograph for the following 1000-m reach segment.(use 4 decimal places for the outflow hydrograph to determine the routing time to reach the 0m3/s)(As you could submit your routing in Excel, hand/typing calculation sare required for the time step that corresponds to your last digit of the net id. If 0 then 10th time step

d.(5 pts) Determine the lag time and peak flow attenuation(difference) observed between inflow and outflow hydrographs.e.(5 pts) Is the runoff volume and the runoff depth changing along the reach? Validate your response with proper calculations and demonstrations.

f.(5 pts) Plot all three hydrographs in one same graph.

A semiprofessional baseball team near your town plays two home games each month at the local baseball park. The team splits the concessions 50/50 with the city but keeps all the revenue from ticket sales. The city charges the team $500  each month for the three-month season. The team pays the players and manager a total of $2500 each month. The team charges $10 for each ticket, and the average customer spends $7 at the concession stand. Attendance averages 100 people at each home game.

Part 1. The team earns an average of $________________ in revenue for each game and $______________ of revenue each season.

With total costs of $_____________ each season, the team finishes the season with $________________ of profit.

Part 2   In order to break even, the team needs to sell   tickets for each game. Round to the nearest whole number.

4. A small town has been cryogenically frozen since 2014.When they thaw out, they want to know how their tax rates have changed after the Tax Cuts and Jobs Act of 2017. In all cases assume the standard deduction is taken and personal exemptions are taken for everyone in the household.a. Mo earns $90,000. He is a single filer. What is his average tax rate in 2014 versus in 2019?b. Elaina earns $90,000. She is married, and files as a married couples filing jointly with her spouse who earns no income. What is her average tax rate in 2014 versus in 2019? c.Meriam earns $90,000. She files as a head of household with four dependents. What is her average tax rate in 2014 versus in 2019?d. Based on this example, what demographic has benefitted the most from the changes in the Tax Cuts and Jobs Act of 2017?

You are a second year student in Prestige Open University. The recent pandemic, Covid-19, has forced your university to move lessons online. This change brought about relief to some students but also some challenges to others. As a second year student, you have decided to write a proposal to the dean of the school to highlight the problems faced and suggest some possible solutions.

In your proposal to the dean of the school,
 state the purpose of your proposal;
 suggest two (2) problems that you faced while attending classes online;
 suggest two (2) solutions to overcome those problems; and
 describe the benefits of those suggestions to the students.

Your proposal should be about 600-800 words.

1. A researcher is interested in finding out if college-bound high school students tend to smoke cigarettes less than high school students who are not college-bound. He distributes a questionnaire and finds that for a group of 57 college-bound students, the mean number of cigarettes smoked per week is 4.0 with a standard deviation of 2.0. For 36 non-college-bound students, he finds that the mean number of cigarettes smoked per week is 9.0 with a standard deviation of 3.0. A. What is the null hypothesis? B. What is the alternative hypothesis? C. What is the t value? (Be sure to show your work.) D. Using your table, is the difference between these groups statistically significant at the 0.05 level?

Question 4)

Schools in Indonesia regularly measure the height and weight of primary school kids to compute their body mass index (BMI) in evaluating potential problems with their health. Heights of primary school kids in Indonesia are normally distributed with a mean of 125cm and a standard deviation of 15cm.

a) Find the probability that a randomly selected kid would have a height more than 142cm. Display working.

b) Find the probability that the mean height for five randomly selected kids is less than 128cm. Display working.

c) Six kids are randomly selected. What is the probability that their mean height is between 120cm and 125cm? Display working.

d) Find the cut off height for the 3% shortest kids. Display working.

Schools in Indonesia regularly measure the height and weight of primary school kids to compute their body mass index (BMI) in evaluating potential problems with their health.
Heights of primary school kids in Indonesia are normally distributed with a mean of 125cm and a standard deviation of 15cm.

a) Find the probability that a randomly selected kid would have a height more than 142cm. Display working.

b) Find the probability that the mean height for five randomly selected kids is less than 128cm. Display working.

c) Six kids are randomly selected. What is the probability that their mean height is between 120cm and 125cm? Display working.

d) Find the cut off height for the 3% shortest kids. Display working.

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 22 scores from all of the students who took the test. She sees that the mean score is 160 with a standard deviation of 28.2396. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 28. Is there evidence that the standard deviation of test scores has increased at the α=0.005 level? Assume the population is normally distributed. Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

2. For each of the following situations, write down

(a) the most appropriate graphical display for the data, and (b) identify a statistic that you might be interested in regarding the data.

(i) [2 marks] A survey given to 400 high school students asked the following question: "How many minutes do you study on a typical weeknight?".

(ii) [2 marks] Students in Statistics classes made up of 360 students were asked the main method of transportation to school. Students answers were: Canada Line/Skytrain, Cycling, Car, Bus, Walk.

(iii) [2 marks] The wait time in minutes before a caller gets to speak to a live agent at a Call Centre is collected for 50 telephone calls.